**1.** A ball hits the floor and rebounds after inelastic collision. In this case

**Ans: **The total momentum of the ball and the earth is conserved

**Solution**

By the conservation of momentum in the absence of external force total momentum of the system (ball + earth) remains constant.

**2.** A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is

**Ans:** MgL/18

**Solution **

**3. **If W_{1}, W_{2} and W_{3} represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W_{1}, W_{2} and W_{3}

**Ans: **W_{3}

**Solution:**

Gravitational force is a conservative force and work done against it is a point function i.e. does not depend on the path.

**4.** A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to -K/r^{2} , where K is a constant. The total energy of the particle is

**Ans: **

**Solution:**:

**5. **The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation , where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is

**Ans: **0 J

**Solution:**

**6.** A force F = -K(yi + xj) _{ }(where K is a positive constant) acts on a particle moving in the XY-plane. Starting from the origin, the particle is taken along the positive X-axis to the point (a, 0) and then parallel to the Y-axis to the point (a, a). The total work done by the force F on the particles is

**Ans:** _{ -Ka2}

**Solution:**

While moving from (0, 0) to (a, 0)

Along positive X-axis, y = 0

i.e. force is in negative Y-direction while displacement is in positive X-direction.

W_{1} = 0

Because force is perpendicular to displacement

Then particle moves from (a, 0) to (a, a) along a line parallel to Y-axis (x = +a) during this

The first component of force, _{ }will not contribute any work because this component is along negative X-direction _{ }while displacement is in positive Y-direction (a, 0) to (a, a). The second component of force i.e. will perform negative work

**7.** If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is

**Ans:**

**Solution: **

**8. **A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then

**Ans:** Both come to rest in a same distance

**Solution: **

If lorry and car both possess same kinetic energy and retarding force is also equal then both come to rest in the same distance.

**9. **A particle free to move along the X-axis has potential energy given by _{ }for , where k is a positive constant of appropriate dimensions. Then

**Ans:** For small displacements from x = 0, the motion is simple harmonic

**Solution:**

**10.** The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to

**Ans: **Independent of m

**Solution:**

Kinetic energy acquired by the body

= Force applied on it × Distance covered by the body

K.E. = F × d

If F and d both are same then K.E. acquired by the body will be same

**11. **An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is

**Ans: **

**Solution: **

**12.** Consider the following two statements

1. Linear momentum of a system of particles is zero

2. Kinetic energy of a system of particles is zero

Then

**Ans: **1 does not imply 2 but 2 implies 1

**Solution:**

Because linear momentum is vector quantity where as kinetic energy is a scalar quantity.

**13.** A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

**Ans: ** _{t 3/2}

**Solution: **

**14. **A shell is fired from a cannon with velocity v m/sec at an angle with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in m/sec of the other piece immediately after the explosion is

**Ans: _{ 3 v cos}**

_{ }**Solution:**

Shell is fired with velocity v at an angle with the horizontal.

So its velocity at the highest point = horizontal component of velocity = vcos

So momentum of shell before explosion = mvcos

When it breaks into two equal pieces and one piece retrace its path to the canon, then other part move with velocity V.

**15.** A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity 30 meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be

**Ans:** _{ }and 135° from either

**Solution:**

Let two pieces are having equal mass m and third piece have a mass of 3m.

According to law of conservation of linear momentum. Since the initial momentum of the system was zero, therefore final momentum of the system must be zero i.e. the resultant of momentum of two pieces must be equal to the momentum of third piece. We know that if two particle possesses same momentum and angle in between them is 90° then resultant will be given by

Let the velocity of mass 3m is V. So

.^{.}. and angle 135° from either.

(as it is clear from the figure)

**16.** Two particles of masses m_{1} and m_{2} in projectile motion have velocities and respectively at time t = 0. They collide at time t_{0} . Their velocities become and at time while still moving in air. The value of is

**Ans: **

**Solution:**

The momentum of the two-particle system, at t = 0 is

Collision between the two does not affect the total momentum of the system.

A constant external force (m_{1} + m_{2})g acts on the system.

**17.** Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles θ_{1} and θ_{2} respectively with the initial direction of motion. The sum of the angles is

**Ans: **90º

**Solution:**

If the masses are equal and target is at rest and after collision both masses moves in different direction. Then angle between direction of velocity will be 90°, if collision is elastic.

**18. **A body of mass m moving with velocity v collides head on with another body of mass 2m which is initially at rest. The ratio of K.E. of colliding body before and after collision will be

**Ans: **9 : 1

**Solution:**

** **

**19. **A particle P moving with speed v undergoes a head -on elastic collision with another particle Q of identical mass but at rest. After the collision

**Ans: **P comes to rest and Q moves forward with speed v

**20. **A set of n identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is L. The block at one end is given a speed v towards the next one at time t = 0 . All collisions are completely inelastic, then

(a) The last block starts moving at

(b) The last block starts moving at

(c) The centre of mass of the system will have a final speed v

(d) The centre of mass of the system will have a final speed

Ans: b, d

Solution:

Since collision is perfectly inelastic so all the blocks will stick together one by one and move in a form of combined mass.

Time required to cover a distance ‘L’ by first block

Now first and second block will stick together and move with v/2 velocity (by applying conservation of momentum) and combined system will take time to reach up to block third.

Now these three blocks will move with velocity v/3 and combined system will take time to reach upto the block fourth.

So, total time and velocity of combined system having n blocks as .

**21. **How much work does a pulling force of 40 N do on the 20 kg box in pulling it 8 m across the floor at a constant speed. The pulling force is directed at 60° above the horizontal

**Ans: **160 J

**Solution: **

**22. **A horizontal force of 5 N is required to maintain a velocity of 2 m/s for a block of 10 kg mass sliding over a rough surface. The work done by this force in one minute is

**Ans: **600 J

**Solution: **

**23. **Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t_{1} as a function of time t is given by

**Ans:
Solution:**

**24. **What is the shape of the graph between the speed and kinetic energy of a body?

**Ans:** Parabola

**Solution:**

Kinetic energy

It means the graph between the speed and kinetic energy will parabola

**25. **When a body moves with some friction on a surface

**Ans: **Kinetic energy and momentum both decrease

**Solution: **Friction is a non-conservative external force to the system, it decreases momentum and kinetic energy both.

**26. **A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M. If the block rises to a height h, the initial velocity of the block will be

**Ans:
Solution:**

**27. **There will be decrease in potential energy of the system, if work is done upon the system by

**Ans: **A conservative force

**28. **The slope of kinetic energy displacement curve of a particle in motion is

**Ans: **Directly proportional to the acceleration

**Solution:**

**29. **The energy required to accelerate a car from 10 m/s to 20 m/s is how many times the energy required to accelerate the car from rest to 10 m/s

**Ans: **3 times

**Solution:**

**30. **A body of mass 2 kg slides down a curved track which is quadrant of a circle of radius 1 metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is

**Ans: **4.43 m/sec

**Solution:**

**31. **The kinetic energy of a body decreases by 36%. The decrease in its momentum is

**Ans: **20%

**Solution:**

**32. **A bomb of mass 3m kg explodes into two pieces of mass m kg and 2m kg. If the velocity of m kg mass is 16 m/s, the total kinetic energy released in the explosion is

**Ans: **192 mJ

**Solution:**

**33. **Which one of the following statement does not hold good when two balls of masses m_{1} and m_{2} undergo elastic collision

(a) When m_{1} << m_{2} and m_{2} at rest, there will be maximum transfer of momentum

(b) When m_{1} >> m_{2} and m_{2} at rest, after collision the ball of mass m_{2} moves with four times the velocity of m_{1}

(c) When m_{1} = m_{2 }and m_{2} at rest, there will be maximum transfer of K.E.

(d) When collision is oblique and m_{2} at rest with m_{1} = m_{2}, after collision the balls move in opposite directions

**Ans: **b, d

**Solution:**

When m_{1} > m_{2} and m_{2} at rest, after collision the ball of mass m_{2} moves with double the velocity of u_{1}. So option (b) is incorrect.

When collision is oblique and m_{2} at rest with m_{1 }=_{ }m_{2} , after collision the ball moves in perpendicular direction. So option (d) is also incorrect.

**34. **A neutron travelling with a velocity v and K.E. E collides perfectly elastically head on with the nucleus of an atom of mass number A at rest. The fraction of total energy retained by neutron is

**Ans:
Solution:**

**35. **A body of mass m_{1} moving with uniform velocity of 40 m/s collides with another mass m_{2} at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses is

**Ans:** 3.0

**Solution:**

**36. **Six identical balls are lined in a straight groove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity v collide elastically with the row of 6 balls from left. What will happen?

**Ans: **Two balls from the right roll out with speed v each and the remaining balls will remain stationary.

**Solution: **Momentum and kinetic energy is conserved only in this case.

**37. **A wooden block of mass M rests on a horizontal surface. A bullet of mass m moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance x on the surface. If the coefficient of friction between wood and the surface is µ , the speed of the bullet at the time of striking the block is (where m is mass of the bullet)

**Ans:
Solution:**

**38. **A ball moving with speed v hits another identical ball at rest. The two balls stick together after collision. If specific heat of the material of the balls is S, the temperature rise resulting from the collision is

**Ans:
Solution:**

**39. **A bag of sand of mass M is suspended by a string. A bullet of mass m is fired at it with velocity v and gets embedded into it. The loss of kinetic energy in this process is

**Ans: **

**Solution:**

After inelastic collision system moves with velocity V

By the conservation of momentum

**Graphical Questions **

**40. **A batsman hits a sixer and the ball touches the ground outside the cricket ground. Which of the following graph describes the variation of the cricket ball's vertical velocity v with time between the time t_{1} as it hits the bat and time t2 when it touches the ground

**Ans: **

**Solution:**

At time t_{1} the velocity of ball will be maximum and it goes on decreasing with respect to time.

At the highest point of path its velocity becomes zero, then it increases but direction is reversed

**41. **The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is

**Ans: **20 ergs

**Solution: **Work done = area between the graph and position axis

**42. **The pointer reading v/s load graph for a spring balance is as given in the figure. The spring constant is

**Ans: **0.1 kg/cm

**Solution:**

**43. **A force-time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and 8 second is

**Ans: **

**Solution: **As the area above the time axis is numerically equal to area below the time axis therefore net momentum gained by body will be zero because momentum is a vector quantity.

**44. **Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x = 0 to x = 35 m is equal to

**Ans: **287.5 J

**Solution:**

**45.** A 10kg mass moves along X-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x = 0 to x = 8 cm?

**Ans: **

**Solution:**

Work done = Area covered in between force displacement curve and displacement axis

= Mass × Area covered in between acceleration-displacement curve and displacement axis.

**46. **A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement x. The maximum height attained is given by

**Ans:** y_{max} = 11 m

**Solution:**

**47. **The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and initial velocity is 2 m/s. When the distance covered by the body is 4m, its kinetic energy would be

**Ans:** 10 J

**Solution:**

**48.** A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at x = 0, its velocity at x = 12 m is

**Ans: **40 m /s

**Solution:**

**49. **The relation between the displacement X of an object produced by the application of the variable force F is represented by a graph shown in the figure. If the object undergoes a displacement from X = 0.5 m to X = 2.5 m the work done will be approximately equal to

**Ans: **16 J

**Solution:**

Work done = Area under curve and displacement axis

= Area of trapezium

As the area actually is not trapezium so work done will be more than 14 J i.e. approximately 16 J

**50. **A particle is dropped from a height h. A constant horizontal velocity is given to the particle. Taking g to be constant every where, kinetic energy E of the particle w. r. t. time t is correctly shown in

**Ans: **

**Solution:**

As particle is projected with some velocity therefore its initial kinetic energy will not be zero.

As it moves downward under gravity then its velocity increases with time K.E. ∝ v^{2} ∝ t^{2 } (As u ∝ t)

So the graph between kinetic energy and time will be parabolic in nature.

**51. **The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from

**Ans:** A to B

**Solution:** From the graph it is clear that force is acting on the particle in the region AB and due to this force kinetic energy (velocity) of the particle increases. So the work done by the force is positive.

**52. **A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = -kx + ax^{3}. Here k and a are positive constants. For x ≥ 0, the functional form of the potential energy U (x) of the particle is

**Ans: **

**Solution:**

**53. **A force F acting on an object varies with distance x as shown here. The force is in newton and x in metre. The work done by the force in moving the object from x = 0 to x = 6m is

**Ans: **13.5 J

**Solution:**

**54. **The potential energy of a system is represented in the first figure. The force acting on the system will be represented by

**Ans: **

**Solution: **As slope of problem graph is positive and constant upto certain distance and then it becomes zero.

So from , up to distance a, F = constant (negative) and becomes zero suddenly.

**55. **A particle, initially at rest on a frictionless horizontal surface, is acted upon by a horizontal force which is constant in size and direction. A graph is plotted between the work done (W) on the particle, against the speed of the particle, (v). If there are no other horizontal forces acting on the particle the graph would look like

**Ans: **

**Solution:**

Work done = change in kinetic energy

graph will be parabolic in nature

**56. **Which of the following graphs is correct between kinetic energy (E), potential energy (U) and height (h) from the ground of the particle

**Ans: **

**Solution: **Potential energy increases and kinetic energy decreases when the height of the particle increases it is clear from the graph .

**57. **The graph between and is (E =kinetic energy and p = momentum)

**Ans: **

**Solution:**

**58. **The force acting on a body moving along X-axis varies with the position of the particle as shown in the fig.

The body is in stable equilibrium at

**Ans: **x = x_{2}

**Solution:**

When particle moves away from the origin then at position x = x_{1} force is zero and at x > x_{1}, force is positive (repulsive in nature) so particle moves further and does not return back to original position.

i.e. the equilibrium is not stable.

Similarly at position x = x_{2} force is zero and at x > x_{2}, force is negative (attractive in nature)

So particle return back to original position i.e. the equilibrium is stable

**59. **The potential energy of a particle varies with distance x as shown in the graph.

The force acting on the particle is zero at

** Ans:** B and C

**Solution:**

it is clear that slope of U – x curve is zero at point B and C. F = 0 for point B and C

**60. **Figure shows the F-x graph. Where F is the force applied and x is the distance covered

by the body along a straight line path. Given that F is in newton and x in metre, what is the work done ?

**Ans: **10 J

**Solution:**

Work done = area under curve and displacement axis

=

**61. **The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length, the line OA will

**Ans: **Shift towards F-axis

**Solution:**

When the length of spring is halved, its spring constant will becomes double. (because )

Slope of force displacement graph gives the spring constant (k) of spring.

If k becomes double then slope of the graph increases

i.e. graph shifts towards force-axis.

**62. **The graph between E and v is

**Ans: **

**Solution:**

**63. **A particle of mass m moving with a velocity u makes an elastic one dimensional collision with a stationary particle of mass m establishing a contact with it for extremely small time T.

Their force of contact increases from zero to F_{0} linearly in time , remains constant for a further time and decreases linearly from F_{0} to zero in further time as shown. The magnitude possessed by F_{0} is

**Ans: **

**Solution:**

**64. **A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x ?

**Ans: **

**Solution:**

When body moves under action of constant force then kinetic energy acquired by the body K.E. = F × S

**65. **The diagrams represent the potential energy U of a function of the inter-atomic distance r. Which diagram corresponds to stable molecules found in nature?

**Ans: **

**Solution:**

When the distance between atoms is large then interatomic force is very weak. When they come closer, force of attraction increases and at a particular distance force becomes zero. When they are further brought closer force becomes repulsive in nature.

This can be explained by slope of curve shown in graph.

**66**. The relationship between the force F and position x of a body is as shown in figure. The work done in displacing the body from x = 1 m to x = 5 m will be

**Ans: **15 J

**Solution:**

**67. **A particle is placed at the origin and a force F = kx is acting on it (where k is positive constant). If U(0) = 0, the graph of U(x) versus x will be (where U is the potential energy function)

**Ans: **

**Solution:**

This is the equation of parabola symmetric to U axis in negative direction

**Assertion & Reason**

Read the assertion and reason carefully to mark the correct option out of the options given below:

(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(c) If assertion is true but reason is false.

(d) If the assertion and reason both are false.

(e) If assertion is false but reason is true.

**67. **Assertion : A person working on a horizontal road with a load on his head does no work.

Reason : No work is said to be done, if directions of force and displacement of load are perpendicular to each other.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution:**

The work done, , when a person walk on a horizontal road with load on his head then .

Hence

Thus no work is done by the person.

**68. **Assertion : The work done during a round trip is always zero.

Reason : No force is required to move a body in its round trip.

**Ans: **If the assertion and reason both are false.

**Solution: **In a round trip work done is zero only when the force is conservative in nature.

Force is always required to move a body in a conservative or non-conservative field

**69. **Assertion : Work done by friction on a body sliding down an inclined plane is positive.

Reason : Work done is greater than zero, if angle between force and displacement is acute or both are in same direction.

**Ans: **If assertion is false but reason is true.

**Solution: **When a body slides down on inclined plane,

work done by friction is negative because it opposes the motion (θ = 180° between force and displacement)

**70. **Assertion : When a gas is allowed to expand, work done by gas is positive.

Reason : Force due to gaseous pressure and displacement (of piston) are in the same direction.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **Since the gaseous pressure and the displacement (of piston) are in the same direction. Therefore θ = 0º

Thus during expansion work done by gas is positive.

**71. **Assertion : A light body and heavy body have same momentum. Then they also have same kinetic energy.

Reason : Kinetic energy does not depend on mass of the body.

**Ans:** If the assertion and reason both are false.

**Solution:**

When two bodies have same momentum then lighter body possess more kinetic energy because

when P = constant

**72. **Assertion : The instantaneous power of an agent is measured as the dot product of instantaneous velocity and the force acting on it at that instant.

Reason : The unit of instantaneous power is watt

**Ans: **If both assertion and reason are true but reason is not the correct explanation of the assertion.

**Solution: **

**73. **Assertion : The change in kinetic energy of a particle is equal to the work done on it by the net force.

Reason : Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.

**Ans: **If assertion is true but reason is false.

**Solution: **Change in kinetic energy = work done by net force. This relationship is valid for particle as well as system of particles.

**74. **Assertion : A spring has potential energy, both when it is compressed or stretched.

Reason : In compressing or stretching, work is done on the spring against the restoring force.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **The work done on the spring against the restoring force is stored as potential energy in both conditions when it is compressed or stretched.

**75. **Assertion : Comets move around the sun in elliptical orbits. The gravitational force on the comet due to sun is not normal to the comet’s velocity but the work done by the gravitational force over every complete orbit of the comet is zero.

Reason : Gravitational force is a non conservative force.

**Ans: **If assertion is true but reason is false.

**Solution: **The gravitational force on the comet due to the sun is a conservative force. Since the work done by a conservative force over a closed path is always zero (irrespective of the nature of path), the work done by the gravitational forces over every complete orbit of the comet is zero.

**76. **Assertion : The rate of change of total momentum of a many particle system is proportional to the sum of the internal forces of the system.

Reason : Internal forces can change the kinetic energy but not the momentum of the system.

**Ans: **If assertion is false but reason is true.

**Solution: **Rate of change of momentum is proportional to external forces acting on the system. The total momentum of whole system remain constant when no external force is acted upon it. Internal forces can change the kinetic energy of the system.

**77. **Assertion : Water at the foot of the water fall is always at different temperature from that at the top.

Reason : The potential energy of water at the top is converted into heat energy during falling.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **When the water is at the top of the fall it has potential energy mgh (where m is the mass of the water and h is the height of the fall). On falling, this potential energy is converted into kinetic energy, which further converted into heat energy and so temperature of water increases.

**78. **Assertion : The power of a pump which raises 100 kg of water in 10sec to a height of 100 m is 10 KW.

Reason : The practical unit of power is horse power.

**Ans: **If both assertion and reason are true but reason is not the correct explanation of the assertion.

**Solution: **The power of the pump is the work done by it per sec.

**79.** Assertion : According to law of conservation of mechanical energy change in potential energy is equal and opposite to the change in kinetic energy.

Reason : Mechanical energy is not a conserved quantity.

**Ans: **If assertion is true but reason is false.

**Solution: **For conservative forces the sum of kinetic and potential energies at any point remains constant throughout the motion. This is known as law of conservation of mechanical energy. According to this law,

Kinetic energy + Potential energy = constant

**80. **Assertion : When the force retards the motion of a body, the work done is zero.

Reason : Work done depends on angle between force and displacement.

**Ans: **If assertion is false but reason is true.

**Solution: **When the force retards the motion, the work done is negative. Work done depends on the angle between force and displacement

**81. **Assertion : In an elastic collision of two bodies, the momentum and energy of each body is conserved.

Reason : If two bodies stick to each other, after colliding, the collision is said to be perfectly elastic.

**Ans: **If the assertion and reason both are false.

**Solution: **In an elastic collision both the momentum and kinetic energy remains conserved. But this rule is not for individual bodies, but for the system of bodies before and after the collision. While collision in which there occurs some loss of kinetic energy is called inelastic collision. Collision in daily life are generally inelastic. The collision is said to be perfectly inelastic, if two bodies stick to each other.

**82. **Assertion : A body cannot have energy without having momentum but it can have momentum without having energy.

Reason : Momentum and energy have same dimensions.

**Ans: **If the assertion and reason both are false.

**Solution: **A body can have energy without having momentum if it possess potential energy but if body possess momentum then it must posses kinetic energy. Momentum and energy have different dimensions.

**83. **Assertion : Power developed in circular motion is always zero.

Reason : Work done in case of circular motion is zero.

**Ans: **If assertion is false but reason is true.

**Solution: **Work done and power developed is zero in uniform circular motion only.

**84. **Assertion : A kinetic energy of a body is quadrupled, when its velocity is doubled.

Reason : Kinetic energy is proportional to square of velocity.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **

If velocity is doubled then K.E. will be quadrupled.

**85.** Assertion : A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical.

Reason : The rate of change of momentum determine that force is small or large.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **In a quick collision, time t is small. As F t = constant, therefore, force involved is large, i.e. collision is more violent in comparison to slow collision.

**86. **Assertion : Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.

Reason : Gravitational forces are conservative forces.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **From, definition, work done in moving a body against a conservative force is independent of the path followed.

**87. **Assertion : Wire through which current flows gets heated.

Reason : When current is drawn from a cell, chemical energy is converted into heat energy.

**Ans: **If assertion is true but reason is false.

**Solution: **When we supply current through the cell, chemical reactions takes place, so chemical energy of cell is converted into electrical energy. If a large amount of current is drawn from wire for a long time only then wire get heated.

**88. **Assertion : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.

Reason : Potential energy of a stretched or compressed spring, proportional to square of extension or compression.

**Ans: **If assertion is false but reason is true.

**Solution:**

Potential energy

This is a equation of parabola, so graph between U and x is a parabola, not straight line.

**89. **Assertion : Heavy water is used as moderator in nuclear reactor.

Reason : Water cool down the fast neutron.

**Ans: **If assertion is true but reason is false.

**Solution: **When two bodies of same mass undergo an elastic collision, their velocities get interchanged after collision. Water and heavy water are hydrogenic materials containing protons having approximately the same mass as that of a neutron. When fast moving neutrons collide with protons, the neutrons come to rest and protons move with the velocity of that of neutrons.

**90. **Assertion : Mass and energy are not conserved separately, but are conserved as a single entity called mass-energy.

Reason : Mass and energy conservation can be obtained by Einstein equation for energy.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **From Einstein equation

it can be observed that if mass is conserved then only energy is conserved and vice versa. Thus, both cannot be treated separately.

**91. **Assertion : If two protons are brought near one another, the potential energy of the system will increase.

Reason : The charge on the proton is + 1.6 × 10^{-19} C.

**Ans: **If both assertion and reason are true but reason is not the correct explanation of the assertion.

**Solution: **If two protons are brought near one another, work has to be done against electrostatic force because same charge repel each other. This work done is stored as potential energy in the system.

**92. **Assertion : In case of bullet fired from gun, the ratio of kinetic energy of gun and bullet is equal to ratio of mass of bullet and gun.

Reason : In firing, momentum is conserved.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution:**

**93. **Assertion : Power of machine gun is determined by both, the number of bullet fired per second and kinetic energy of bullets.

Reason : Power of any machine is defined as work done (by it) per unit time

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **K.E. of one bullet = k K.E. of n bullet = nk

According to law of conservation of energy, the kinetic energy of bullets be equal to the work done by machine gun per sec.

**94. **Assertion : A work done in moving a body over a closed loop is zero for every force in nature.

Reason : Work done does not depend on nature of force.

**Ans: **If the assertion and reason both are false.

**Solution: **Work done in the motion of a body over a closed loop is zero only when the body is moving under the action of conservative forces (like gravitational or electrostatic forces). i.e. work done depends upon the nature of force.

**95. **Assertion : Mountain roads rarely go straight up the slope.

Reason : Slope of mountains are large therefore more chances of vehicle to slip from roads.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **If roads of the mountain were to go straight up, the slope θ would have been large, the frictional force would be small. Due to small friction, wheels of vehicle would slip. Also for going up a large slope, a greater power shall be required.

**96. **Assertion : Soft steel can be made red hot by continued hammering on it, but hard steel cannot.

Reason : Energy transfer in case of soft iron is large as in hard steel.

**Ans: **If both assertion and reason are true and the reason is the correct explanation of the assertion.

**Solution: **The rise in temperature of the soft steel is an example of transferring energy into a system by work and having it appear as an increase in the internal energy of the system. This works well for the soft steel because it is soft. This softness results in a deformation of the steel under blow of the hammer. Thus the point of application of the force is displaced by the hammer and positive work is done on the steel. With the hard steel, less deformation occur, thus, there is less displacement of point of application of the force and less work done on the steel. The soft steel is therefore better in absorbing energy from the hammer by means of work and its temperature rises more rapidly.