**1.** A vessel containing water is given a constant acceleration a towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid

**Ans:** C

**Sol:**

Due to acceleration in forward direction, vessel is an accelerated frame therefore a Pseudo force will be exerted in backward direction. Therefore water will be displaced in backward direction.

**2. **A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

**Ans:** Lower in front side

**Sol: **The pressure on the rear side would be more due to fictitious force (acting in the opposite direction of acceleration) on the rear face. Consequently the pressure in the front side would be lowered.

**3.** A ship of mass _{ }initially at rest is pulled by a force of _{ }through a distance of 3 m. Assume that the resistance due to water is negligible, the speed of the ship is

**Ans:** 0.1 m/s

**Sol: **

**4.** The mass of a body measured by a physical balance in a lift at rest is found to be m. If the lift is going up with an acceleration a, its mass will be measured as

**Ans:** m

**Sol:**

Mass measured by physical balance remains unaffected due to variation in acceleration due to gravity.

**5.** Three weights W, 2W and 3W are connected to identical springs suspended from a rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that

**Ans:** All will be at the same distance

**Sol: **For W, 2W, 3W apparent weight will be zero because the system is falling freely. So the distances of the weight from the rod will be same.

**6.** When forces F_{1, }F_{2, }F_{3} are acting on a particle of mass m such that F_{2} and F_{3} are mutually perpendicular, then the particle remains stationary. If the force F_{1} is now removed then the acceleration of the particle is

**Ans: **_{ }F_{1/m}

**Sol:**

**7.** The spring balance A reads 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker filled with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid as shown in figure. In this situation

(a) The balance A will read more than 2 kg

(b) The balance B will read more than 5 kg

(c) The balance A will read less than 2 kg and B will read more than 5 kg

(d) The balances A and B will read 2 kg and 5 kg respectively

**Ans:** b, c

**Sol:**

Force of upthrust will be there on mass m shown in figure, so A weighs less than 2 kg. Balance will show sum of load of beaker and reaction of upthrust so it reads more than 5 kg.

**8. **A rocket is propelled by a gas which is initially at a temperature of 4000 K. The temperature of the gas falls to 1000 K as it leaves the exhaust nozzle. The gas which will acquire the largest momentum while leaving the nozzle, is

**Ans:** Argon

**Sol:**

Heavier gas will acquire largest momentum i.e. Argon.

**9. **Consider the following statement: When jumping from some height, you should bend your knees as you come to rest, instead of keeping your legs stiff. Which of the following relations can be useful in explaining the statement. Where symbols have their usual meaning.

**Ans: **

**Sol: **

By doing so time of change in momentum increases and impulsive force on knees decreases

**10.** A false balance has equal arms. An object weigh X when placed in one pan and Y when placed in other pan, then the weight W of the object is equal to

**Ans: **

**Sol:**

When false balance has equal arms then,

**11. **The vector sum of two forces is perpendicular to their vector differences. In that case, the force

**Ans:** Are equal to each other in magnitude

**Sol:**

**12.** In the arrangement shown in figure the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

**Ans: ** _{}

**Sol: **

**13.** The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be

**Ans: **45^{o}

**Sol:**

**14.** A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by

**Ans: **

**Sol: **

**15. **A pulley fixed to the ceilling carries a string with blocks of mass m and 3 m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with what acceleration

**Ans: **

**Sol:**

**16. **A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity . Here t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take g = 10 m/s^{2})

**Ans: **26 N

**Sol:**

**17. **A stick of 1 m is moving with velocity of . What is the apparent length of the stick

**Ans: **0.44 m

**Sol:**

**18. **One day on a spacecraft corresponds to 2 days on the earth. The speed of the spacecraft relative to the earth is

**Ans: **

**Sol:**

**19. **A flat plate moves normally with a speed v_{1} towards a horizontal jet of water of uniform area of cross-section. The jet discharges water at the rate of volume V per second at a speed of v_{2}. The density of water is ρ. Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet of water is

**Ans:**

**Sol:**

**20. **A car is moving with uniform velocity on a rough horizontal road. Therefore, according to Newton's first law of motion

**Ans:** A force is surely being applied by its engine

**Sol:**

Since, force needed to overcome frictional force.

**21. **A person is sitting in a travelling train and facing the engine. He tosses up a coin and the coin falls behind him. It can be concluded that the train is

**Ans: **Moving forward and gaining speed

**Sol:**

The coin falls behind him it means the velocity of train was increasing otherwise the coin fall directly into the hands of thrower.

**22. **A block can slide on a smooth inclined plane of inclination θ kept on the floor of a lift. When the lift is descending with a retardation a, the acceleration of the block relative to the incline is

**Ans: **

**Sol:**

**23. **A 60 kg man stands on a spring scale in the lift. At some instant he finds, scale reading has changed from 60 kg to 50kg for a while and then comes back to the original mark. What should we conclude ?

**Ans: **The lift while in constant motion upwards, is stopped suddenly

**Sol:**

For upward acceleration apparent weight = m(g + a)

If lift suddenly stops during upward motion then apparent weight = m(g - a) because instead of acceleration, we will consider retardation

In the problem it is given that scale reading initially was 60 kg and due to sudden jerk reading decreasing and finally comes back to the original mark i.e., 60 kg.

So, we can conclude that lift was moving upward with constant speed and suddenly stops.

**24. **When a body is acted by a constant force, then which of the following quantities remains constant

**Ans: **Acceleration

**Sol: **

**25. **A man of weight mg is moving up in a rocket with acceleration 4 g. The apparent weight of the man in the rocket is

**Ans: **5 mg

**Sol:**

**26. **A spring balance and a physical balance are kept in a lift. In these balances equal masses are placed. If now the lift starts moving upwards with constant acceleration, then

**Ans: **The reading of spring balance will increase and the physical balance will remain in equilibrium

**Sol: **The fictitious force will act downwards. So the reading of spring balance will increase. In case of physical balance, the fictitious force will act on both the pans, so the equilibrium is not affected.

**27. **As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be

**Ans: **2 kg

**Sol:**

In this case, one 2 kg wt on the left will act as the support for the spring balance. Hence its reading will be 2 kg.

**28. **A player kicks a football of mass 0.5 kg and the football begins to move with a velocity of 10 m/s. If the contact between the leg and the football lasts for sec, then the force acted on the football should be

**Ans: **250 N

**Sol:**

**29. **The engine of a jet aircraft applies a thrust force of 10^{5} N during take off and causes the plane to attain a velocity of 1 km/sec in 10 sec. The mass of the plane is

**Ans: **10^{3} kg

**Sol:**

**30. **A force of 50 dynes is acted on a body of mass 5 g which is at rest for an interval of 3 seconds, then impulse is

**Ans: **

**Sol:**

**31. **Two weights w_{1} and w_{2} are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up at an acceleration g, the tension in the string will be

**Ans: **

**Sol:**

**32. **The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration 12m/sec^{2}. What is the acceleration of 20 kg mass

**Ans: **4m/sec^{2}

**Sol: **As the mass of 10 kg has acceleration 12 m/s^{2} therefore it apply 120N force on mass 20kg in a backward direction.

**33. **Two masses M and m are connected by a weightless string. They are pulled by a force F on a frictionless horizontal surface. The tension in the string will be

**Ans: **

**Sol:**

**34. **In the above question, the acceleration of mass m is

**Ans: **

**Sol: **

**35.** Three weights A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)

**Ans: **

**Sol:**

**Graphical Questions **

**36. **A block B is placed on block A. The mass of block B is less than the mass of block A. Friction exists between the blocks, whereas the ground on which the block A is placed is taken to be smooth. A horizontal force F, increasing linearly with time begins to act on B.

The acceleration α_{A} and α_{B} of blocks A and B respectively are plotted against t. The correctly plotted graph is

**Sol: **If the applied force is less than limiting friction between block A and B, then whole system move with common acceleration

But the applied force increases with time, so when it becomes more than limiting friction between A and B, block B starts moving under the effect of net force F – F_{k}

As F is increasing with time so aB will increase with time

Kinetic friction is the cause of motion of block A

It is clear that a_{B} > a_{A} . i.e. graph (d) correctly represents the variation in acceleration with time for block A and B.

**37. **In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t = 2 sec is

**Ans: **-0.2lkg m sec^{-1}

**Sol:**

**38. **The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to 8 second will be

**Ans: **Zero

**Sol: **Momentum acquired by the particle is numerically equal to area enclosed between the F-t curve and time axis. For the given diagram area in upper half is positive and in lower half is negative (and equal to upper half), so net area is zero. Hence the momentum acquired by the particle will be zero.

**39.** Figure shows the displacement of a particle going along the X-axis as a function of time. The force acting on the particle is zero in the region

(a) AB (b) BC (c) CD (d) DE

**Ans: **a, c

**Sol: **(a, c) In region AB and CD, slope of the graph is constant i.

**40. **A body of 2 kg has an initial speed 5ms–1. A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The final speed of the body.

**Ans: **14.25 ms^{–1}

**Sol:**

**41. **Which of the following graph depicts spring constant k versus length l of the spring correctly

**Ans: **d)

**Sol:**

It means graph between K and l should be hyperbolic in nature.

**42. **A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F0 linearly in time T/2, and decreases linearly to zero in further time T/2. The magnitude of F0 is

**Ans: **2mu/T

**Sol:**

In elastic one dimensional collision particle rebounds with same speed in opposite direction

i.e. change in momentum = 2mu

**43. **A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is a semicircle.

**Ans: **

**Sol: **Initially particle was at rest. By the application of force its momentum increases.

Final momentum of the particle = Area of F - t graph

**44. **A body of mass 3kg is acted on by a force which varies as shown in the graph below. The momentum acquired is given by

**Ans: **50 N-s

**Sol:**

**45. **The variation of momentum with time of one of the body in a two body collision is shown in fig. The instantaneous force is maximum corresponding to point

**Ans: **R

**Sol:**

**46. **Figures I, II, III and IV depict variation of force with time

The impulse is highest in the case of situations depicted. Figure

**Ans: **III and IV

**Sol:**

Impulse = Area between force and time graph and it is maximum for graph (III) and (IV)

**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.

**1. **Assertion : Inertia is the property by virtue of which the body is unable to change by itself the state of rest only.

Reason : The bodies do not change their state unless acted upon by an unbalanced external force.

**Ans: **e

**Sol:** Inertia is the property by virtue of which the body is unable to change by itself not only the state of rest, but also the state of motion.

**2. **Assertion : If the net external force on the body is zero, then its acceleration is zero.

Reason : Acceleration does not depend on force.

**Ans: **c

**Sol: **According to Newton's second law

Acceleration = i.e. if net external force on the body is zero then acceleration will be zero

**3. **Assertion : Newton’s second law of motion gives the measurement of force.

Reason : According to Newton’s second law of motion, force is directly proportional to the rate of change of momentum.

**Ans: **a

**Sol:**

If we know the values of m and a, the force acting on the body can be calculated and hence second law gives that how much force is applied on the body.

**4. **Assertion : Force is required to move a body uniformly along a circle.

Reason : When the motion is uniform, acceleration is zero.

**Ans:** b

**Sol: **When a body is moving in a circle, its speed remains same but velocity changes due to change in the direction of motion of body. According to first law of motion, force is required to change the state of a body. As in circular motion the direction of velocity of body is changing so the acceleration cannot be zero. But for a uniform motion acceleration is zero (for rectilinear motion).

**5. **Assertion : If two objects of different masses have same momentum, the lighter body possess greater velocity.

Reason : For all bodies momentum always remains same.

**Ans: **c

**Sol: **According to definition of momentum

As velocity is inversely proportional to mass, therefore lighter body possess greater velocity.

**6. **Assertion : Aeroplanes always fly at low altitudes.

Reason : According to Newton’s third law of motion, for every action there is an equal and opposite reaction.

**Ans: **a

**Sol: **The wings of the aeroplane pushes the external air backward and the aeroplane move forward by reaction of pushed air. At low altitudes. density of air is high and so the aeroplane gets sufficient force to move forward.

**7. **Assertion : No force is required by the body to remain in any state.

Reason : In uniform linear motion, acceleration has a finite value.

**Ans: **c

**Sol: **Force is required to change the state of the body. In uniform motion body moves with constant speed so acceleration should be zero.

**8. **Assertion : Mass is a measure of inertia of the body in linear motion.

Reason : Greater the mass, greater is the force required to change its state of rest or of uniform motion.

**Ans: **a

**Sol:** According to Newton’s second law of motion i.e. magnitude of the acceleration produced by a given force is inversely proportional to the mass of the body. Higher is the mass of the body, lesser will be the acceleration produced i.e. mass of the body is a measure of the opposition offered by the body to change a state, when the force is applied i.e. mass of a body is the measure of its inertia.

**9. **Assertion : The slope of momentum versus time curve give us the acceleration.

Reason : Acceleration is given by the rate of change of momentum.

**Ans: **d

**Sol:** Slope of momentum-time graph

i.e. Rate of change of momentum = Slope of momentum- time graph = force.

**10. **Assertion : A cyclist always bends inwards while negotiating a curve.

Reason : By bending, cyclist lowers his centre of gravity.

**Ans: **c

**Sol: **The purpose of bending is to acquire centripetal force for circular motion. By doing so component of normal reaction will counter balance the centrifugal force.

**11. **Assertion : The work done in bringing a body down from the top to the base along a frictionless incline plane is the same as the work done in bringing it down the vertical side.

Reason : The gravitational force on the body along the inclined plane is the same as that along the vertical side.

**Ans: **c

**Sol: **Work done in moving an object against gravitational force (conservative force) depends only on the initial and final position of the object, not upon the path taken. But gravitational force on the body along the inclined plane is not same as that along the vertical and it varies with the angle of inclination.

**12. **Assertion : Linear momentum of a body changes even when it is moving uniformly in a circle.

Reason : Force required to move a body uniformly along a straight line is zero.

**Ans: **b

**Sol: **In uniform circular motion of a body the speed remains constant but velocity changes as direction of motion changes.

As linear momentum = mass × velocity, therefore linear momentum of a body changes in a circle. On the other hand, if the body is moving uniformly along a straight line then its velocity remains constant and hence acceleration is equal to zero. So force is equal to zero.

**13. **Assertion : A bullet is fired from a rifle. If the rifle recoils freely, the kinetic energy of rifle is more than that of the bullet.

Reason : In the case of rifle bullet system the law of conservation of momentum violates.

**Ans: **d

**Sol:** Law of conservation of linear momentum is correct when no external force acts . When bullet is fired from a rifle then both should possess equal momentum but different kinetic

energy. E Kinetic energy of the rifle is less than that of bullet because

**14. **Assertion : A rocket works on the principle of conservation of linear momentum.

Reason : Whenever there is a change in momentum of one body, the same change occurs in the momentum of the second body of the same system but in the opposite direction.

**Ans: **a

**Sol: **As the fuel in rocket undergoes combustion, the gases so produced leave the body of the rocket with large velocity and give upthrust to the rocket. If we assume that the fuel is burnt at a constant rate, then the rate of change of momentum of the rocket will be constant. As more and more fuel gets burnt, the mass of the rocket goes on decreasing and it leads to increase of the velocity of rocket more and more rapidly.

**15. **Assertion : The apparent weight of a body in an elevator moving with some downward acceleration is less than the actual weight of body.

Reason : The part of the weight is spent in producing downward acceleration, when body is in elevator.

**Ans: **c

**Sol:** The apparent weight of a body in an elevator moving with downward acceleration a is given by W = m(g - a)

**16. **Assertion : When the lift moves with uniform velocity the man in the lift will feel weightlessness.

Reason : In downward accelerated motion of lift, apparent weight of a body decreases.

**Ans: **e

**Sol: **For uniform motion apparent weight = Actual weight

For downward accelerated motion,

Apparent weight < Actual weight

**17. **Assertion : In the case of free fall of the lift, the man will feel weightlessness.

Reason : In free fall, acceleration of lift is equal to acceleration due to gravity.

**Ans: **a

**18. **Assertion : A player lowers his hands while catching a cricket ball and suffers less reaction force.

Reason : The time of catch increases when cricketer lowers its hand while catching a ball.

**Ans: **a

**Sol: **By lowering his hand player increases the time of catch, by doing so he experience less force on his hand because

**19. **Assertion : The acceleration produced by a force in the motion of a body depends only upon its mass.

Reason : Larger is the mass of the body, lesser will be the acceleration produced.

**Ans: **b

**Sol: **According to Newton’s second law,

For constant F, acceleration is inversely proportional to mass i.e. acceleration produced by a force depends only upon the mass of the body and for larger mass acceleration will be less.

**20. **Assertion : Linear momentum of a body changes even when it is moving uniformly in a circle.

Reason : In uniform circular motion velocity remain constant.

**Ans: **c

**Sol:** In uniform circular motion, the direction of motion changes, therefore velocity changes.

As P = mv therefore momentum of a body also changes in uniform circular motion.

**21. **Assertion : Newton’s third law of motion is applicable only when bodies are in motion.

Reason : Newton’s third law applies to all types of forces, e.g. gravitational, electric or magnetic forces etc.

**Ans: **e

**Sol: **According to third law of motion it is impossible to have a single force out of mutual interaction between two bodies, whether they are moving or at rest. While, Newton’s third law is applicable for all types of forces.

**22. **Assertion : A reference frame attached to earth is an inertial frame of reference.

Reason : The reference frame which has zero acceleration is called a non inertial frame of reference.

**Ans: **d

**Sol: **An inertial frame of reference is one which has zero acceleration and in which law of inertia hold good i.e. Newton’s law of motion are applicable equally. Since earth is revolving around the sun and earth is rotating about its own axis also, the forces are acting on the earth and hence there will be acceleration of earth due to these factors. That is why earth cannot be taken as inertial frame of reference.

**23. **Assertion : A table cloth can be pulled from a table without dislodging the dishes.

Reason : To every action there is an equal and opposite reaction.

**Ans: **b

**Sol: **According to law of inertia (Newton’s first law), when cloth is pulled from a table, the cloth come in state of motion but dishes remains stationary due to inertia. Therefore when we pull the cloth from table the dishes remains stationary.

**24. **Assertion : A body subjected to three concurrent forces cannot be in equilibrium.

Reason : If large number of concurrent forces acting on the same point, then the point will be in equilibrium, if sum of all the forces is equal to zero.

**Ans: **e

**Sol: **A body subjected to three concurrent forces is found to in equilibrium if sum of these force is equal to zero.

i.e

**25. **Assertion : Impulse and momentum have different dimensions.

Reason : From Newton’s second law of motion, impulse is equal to change in momentum.

**Ans: **e

**Sol: **From Newton's second law

Impulse = Change of momentum.

So they have equal dimensions