**Single Option Questions**

**1.** An Indian rubber cord L metre long and area of cross-section A metre^{2} is suspended vertically. Density of rubber is D kg / metre^{3 }and Young's modulus of rubber is E newton / metre^{2} . If the wire extends by l metre under its own weight, then extension l is

**Ans:** L^{2}Dg / 2E

**2. **To break a wire, a force of 10^{6} N / m^{2} is required. If the density of the material is 3 × 10^{3} kg / m^{3}, then the length of the wire which will break by its own weight will be

**Ans:** 34 m

**Sol: **

**3.** Two rods of different materials having coefficients of linear expansion α_{1}, α_{2} and Young's moduli Y_{1} and Y_{2} respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If

α_{1 }: α_{2} = 2 : 3, the thermal stresses developed in the two rods are equally provided Y_{1} : Y_{2} is equal to

**Ans:** 3 : 2

**Sol:** Thermal stress = YαΔα.

If thermal stress and rise in temperature are equal then

**4. **The extension in a string obeying Hooke's law is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5x, the speed of sound will be

**Ans: **1.22 v

**Sol: **

**5.** One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W_{1} is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height 3L/4 from its lower end is

**Ans: **

_{}

**6. **There are two wires of same material and same length while the diameter of second wire is 2 times the diameter of first wire, then ratio of extension produced in the wires by applying same load will be

Ans: 4 : 1

**7.** A particle of mass m is under the influence of a force F which varies with the displacement x according to the relation F = −kx + F_{0 }in which k and F_{0} are constants. The particle when disturbed will oscillate

**Ans: **_{ }

**8. **An elastic material of Young's modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is**Ans:**

**9.** Two wires A and B of same length, same area of cross-section having the, same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is 3/2 times of that of wire B. The ratio of the forces produced in two wires will be

**Ans: **3/2

**10.** A wire of area of cross-section 10^{−6} m^{2} is increased in length by 0.1%. The tension produced is 1000 N. The Young's modulus of wire is

**Ans: **10^{12} N / m^{2}

**11.** To break a wire of one meter length, minimum 40 kg wt. is required. Then the wire of the same material of double radius and 6 m length will require breaking weight

**Ans: **160 kg-wt

**Sol:** Breaking force = Breaking stress × Area of cross section of wire

Breaking force ∝ r^{2} (Breaking distance is constant) If radius becomes doubled then breaking force will become 4 times i.e. 40 × 4 = 160 kg wt

**12. **The breaking stress of a wire of length L and radius r is 5 kg - wt / m^{2}. The wire of length 2l and radius 2r of the same material will have breaking stress in kg - wt/m^{2}

**Ans: **5

**Sol:** Breaking stress depends on the material of wire.

**13.** The increase in length on stretching a wire is 0.05%. If its Poisson's ratio is 0.4, then its diameter

**Ans:** Reduce by 0.02%

**14. **If Poission's ratio σ is for a material, then the material is

**Ans:** Uncompressible

**15. **If the breaking force for a given wire is F, then the breaking force of two wires of same magnitude will be

**Ans:** 2F

**Sol:** Breaking force ∝ Area of cross section

If area is double then breaking force will become two times.

**16. **If the thickness of the wire is doubled, then the breaking force in the above question will be

**Ans:** 4F

**Sol:** Breaking force ∝ r^{2}

If thickness (radius) of wire is doubled then breaking force will become four times.

**17. **On all the six surfaces of a unit cube, equal tensile force of F is applied. The increase in length of each side will be (Y = Young's modulus, σ = Poission's ratio)**Ans: **

**18.** The mass and length of a wire are M and L respectively. The density of the material of the wire is d. On applying the force F on the wire, the increase in length is l, then the Young's modulus of the material of the wire will be**Ans: ** _{}

19. Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is 0.5 cm, the elongation (l) of each wire is

Y_{s} (steel) = 2.0 × 10^{11} N / m^{2}

Y_{c} (copper) = 1.2 × 10^{11} N / m^{2} **Ans: **l_{s} = 0.75 cm, l_{c} = 1.25 cm

**20.** If the compressibility of water is σ per unit atmospheric pressure, then the decrease in volume V due to P atmospheric pressure will be**Ans:** σ PV

**21.** A rectangular block of size 10cm × 8cm × 5cm is kept in three different positions P, Q and R in turn as shown in the figure. In each case, the shaded area is rigidly fixed and a definite force F is applied tangentially to the opposite face to deform the block. The displacement of the upper face will be

**Ans:**Maximum in R position

For maximum displacement area at which force applied should be minimum and vertical side should be maximum, this is given in the R position of rectangular block.

**Graphical Questions
22. **The graph shown was obtained from experimental measurements of the period of oscillations T for different masses M placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the

**Ans:**Mass of the pan was neglected

If we draw a graph between T

^{2}and M then it will be straight line.

and for M = 0, T

^{2}= 0

i.e. the graph should pass through the origin.

but from the it is not reflected it means the mass of pan was neglected.

**23.** A graph is shown between stress and strain for a metal. The part in which Hooke's law holds good is

**Ans: **OA

**24. **In the graph, point B indicates**Ans: **Yield point

**25. **In the graph, point D indicates**Ans: **Breaking point

**26.** The strain-stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that

a) Elasticity of wire P is maximum b) Elasticity of wire Q is maximum

c) Tensile strength of R is maximum d) None of the above is true

**Ans: **None of the above is true

**27. **The diagram shows a force-extension graph for a rubber band. Consider the following statements

I. It will be easier to compress this rubber than expand it

II. Rubber does not return to its original length after it is stretched

III. The rubber band will get heated if it is stretched and released

Which of these can be deduced from the graph**Ans: **III only **Sol: **Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating.

**28. **The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If YA and YB are the Young ‘s modulii of the materials, then

**Ans: **YA = 3YB

**29. **The load versus elongation graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line

**Ans: **OD

i.e. for the same load, thickest wire will show minimum elongation. So graph D represent the thickest wire.

**30. **The adjacent graph shows the extension (l) of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is 10^{-6} m^{2}, calculate the young’s modulus of the material of the wire

**Ans:**2 × 10

^{11}N / m

^{2}

**31. **The graph is drawn between the applied force F and the strain (x) for a thin uniform wire. The wire behaves as a liquid in the part

**Ans: **bc**Sol: **At point b, yielding of material starts.

**32. **The graph shows the behaviour of a length of wire in the region for which the substance obeys Hook’s law. P and Q represent

**Ans:**P = extension, Q = stored elastic energy

**Sol:**Graph between applied force and extension will be straight line because in elastic range, Applied force µ extension but the graph between extension and stored elastic energy will be parabolic in nature

**33. **The potential energy U between two molecules as a function of the distance X between them has been shown in the figure. The two molecules are

**Ans:**Attracted when x lies between B and C and are repelled when X lies between A and B

**Sol:**

In the region BC slope of the graph is positive

.

^{.}. F = negative i.e. force is attractive in nature

In the region AB slope of the graph is negative

.

^{.}. F = positive i.e. force is repulsive in nature

**34. **The value of force constant between the applied elastic force F and displacement will be

**Ans: **

**35. **The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that

**Ans: **A is ductile and B is brittle**Sol:** In ductile materials, yield point exist while in Brittle material, failure would occur without yielding.

**36. **Which one of the following is the Young’s modulus (in N/m^{2}) for the wire having the stress-strain curve shown in the figure

**Ans: **2.0 × 10^{11}

**37. **The diagram shows the change x in the length of a thin uniform wire caused by the application of stress F at two different temperatures T_{1} and T_{2}. The variations shown suggest that

**Ans: **T_{1} > T_{2}

**Sol: **Elasticity of wire decreases at high temperature i.e. at higher temperature slope of graph will be less.

So we can say that T_{1} > T_{2}

**38. **A student plots a graph from his reading on the determination of Young’s modulus of a metal wire but forgets to label. The quantities on X and Y axes may be respectively.

**Ans: **Stress applied and strain developed

**39. **The points of maximum and minimum attraction in the curve between potential energy (U) and distance (r)of a diatomic molecules are respectively

**Ans: **S and T

**Sol: **Attraction will be minimum when the distance between the molecule is maximum.

Attraction will be maximum at that point where the positive slope is maximum because

**40. **The stress-strain curves for brass, steel and rubber are shown in the figure. The lines A, B and C are for

**Ans: **Steel, brass and rubber respectively

**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.

**41. **Assertion: The stretching of a coil is determined by its shear modulus.

Reason: Shear modulus change only shape of a body keeping its dimensions unchanged. **Ans: **Both assertion and reason are true and the reason is the correct explanation of the assertion.**Sol: **Because, the stretching of coil simply changes its shape without any change in the length of the wire used in coil. Due to which shear modulus of elasticity is involved.

**42. **Assertion: Spring balances show correct readings even after they had been used for a long time interval.

Reason: On using for long time, spring balances losses its elastic strength.**Ans: **Assertion is false but reason is true.**Sol: **When a spring balance has been used for a long time, the spring in the balance fatigued and there is loss of strength of the spring. In such a case, the extension in the spring is more for a given load and hence the balance gives wrong readings.

**43. **Assertion: Steel is more elastic than rubber.

Reason: Under given deforming force, steel is deformed less than rubber.**Ans: **Both assertion and reason are true and the reason is the correct explanation of the assertion.**Sol: **Elasticity is a measure of tendency of the body to regain its original configuration. As steel is deformed less than rubber therefore steel is more elastic than rubber.

**44. **Assertion: Glassy solids have sharp melting point.

Reason: The bonds between the atoms of glassy solids get broken at the same temperature.**Ans: **The assertion and reason both are false.

**Sol: **In a glassy solid (i.e., amorphous solid) the various bonds between the atoms or ions or molecules of a solid are not equally strong. Different bonds are broken at different temperatures. Hence there is no sharp melting point for a glassy solid.

**45. **Assertion: A hollow shaft is found to be stronger than a solid shaft made of same material.

Reason: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.**Ans: **Both assertion and reason are true and the reason is the correct explanation of the assertion.

**46. **Assertion: Bulk modulus of elasticity (K) represents incompressibility of the material.

Reason: Bulk modulus of elasticity is proportional to change in pressure.**Ans:** Both assertion and reason are true and the reason is the correct explanation of the assertion.**Sol: **Bulk modulus of elasticity measures how good the body is to regain its original volume on being compressed. Therefore, it represents incompressibility of the material. where P is increase in pressure, V is change in volume.

**47. **Assertion: Strain is a unitless quantity.

Reason: Strain is equivalent to force.**Ans: **Assertion is true but reason is false.

**Sol: **Strain is the ratio of change in dimensions of the body to the original dimensions. Because this is a ratio, therefore it is dimensionless quantity.

**48. **Assertion: The bridges declared unsafe after a long use.

Reason: Elastic strength of bridges losses with time.**Ans: **Both assertion and reason are true and the reason is the correct explanation of the assertion.**Sol: **A bridge during its use undergoes alternating strains for a large number of times each day, depending upon the movement of vehicles on it when a bridge is used for long time, it losses its elastic strength. Due to which the amount of strain in the bridge for a given stress will become large and ultimately, the bridge may collapse. This may not happen, if the bridges are declared unsafe after long use.

**49. **Assertion: Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Both the balls will rise to same height after bouncing.

Reason: Ivory and wet-clay have same elasticity.**Ans:** The assertion and reason both are false.**Sol: **Ivory is more elastic than wet-clay. Hence the ball of ivory will rise to a greater height. In fact the ball of wet-clay will not rise at all, it will be somewhat flattened permanently.

**50. **Assertion: Young’s modulus for a perfectly plastic body is zero.

Reason: For a perfectly plastic body, restoring force is zero.**Ans: **Both assertion and reason are true and the reason is the correct explanation of the assertion.

**51. **Assertion: Identical springs of steel and copper are equally stretched. More work will be done on the steel spring.

Reason: Steel is more elastic than copper.**Ans: **Both assertion and reason are true and the reason is the correct explanation of the assertion.

Since, elasticity of steel is more than copper, hence more work has to be done in order to stretch the steel.

**52. **Assertion: Sterss is the internal force per unit area of a body.

Reason: Rubber is less elastic than steel.**Ans: **Both assertion and reason are true but reason is not the correct explanation of the assertion.**Sol: **Stress is defined as internal force (restoring force) per unit area of a body. Also, rubber is less elastic than steel, because restoring force is less for rubber than steel.

**Electronic devices, Communication systems**

**1. **If the input and output resistances in a common base amplifier circuit are 400 Ω and 400 kΩ respectively, what is the voltage amplification when the emitter current is 2 mA and current gain α = 0.98?

1) 9.8 2) 98 3) 980 4) 9800

**2. **In a transistor, a change of 8 mA in the emitter current produces a change of 7.8 mA in the collector current. The change in the base current necessary to produce the same change in the collector current is

1) 50 µA 2) 100 µA 3) 150 µA 4) 200 µA

**3. **In a semi conductor, it is found that 4/5 th of the total current is carried by electrons and the remaining 1/5th by the holes. If at this temperature, the drift speed of electrons is 2.5 times that of the holes, the ratio of the number densities of electrons and holes is

1) 1/2 2) 5/8 3) 8/5 4) 2

**4. **A junction diode has a resistance of 25 Ω when forward biased and 2500 Ω when reverse biased. The current in the above arrangements is

**5.** Two diodes D_{1} and D_{2} and two capacitors of capacitances C and 3C are connected as shown in the figure. The output voltage is

1) 3V 2) 6V 3) 9V 4) 12V

**6.**

To obtain the final output X = 1 from the combination of gates P and Q, the inputs A, B and C must be

1) A = 1, B = 0, C = 1 2) A = 1, B = 1, C = 0

3) A = 0, B = 1, C = 0 4) A = 1, B = 0, C = 0

**7. **On one day, the maximum frequency reflected from the ionosphere is 8 MHz. On another day it was found to increase to 9 MHz. Then the ratio of maximum electron densities of the ionosphere on the two days is

**8. **If message signal of frequency 12 kHz and peak voltage 20 V is used to modulate a carrier wave of frequency 12 MHz and peak voltage 30 V. Then the modulation index of the amplitude modulated wave is

1) 10^{-3} 2) 10^{3} 3) 2/3 4) 3/2

**9.**

**10. **Find V0 in the circuit

1) 1.2 V 2) 2.5 V 3) 6 V 4) 6.4 V

**11.** In an n-p-n transistor 1010 electrons enter the emitter in 10^{-6} s. 2% of the electrons are lost in the base. Then the current transfer ratio and the current amplification factor are

1) 0.98, 49 2) 0.88, 49 3) 0.78, 39 4) 0.78, 49

**12. **A p-n-p transistor is used in an amplifier circuit in CE configuration mode. A change of 40 µA in the base current brings a change of 2 mA in collector current and 0.04 V in base - emitter voltage. Then the input resistance (Rin) and base current amplification factor (β) are

1) 1000 Ω, 50 2) 1000 Ω, 100 3) 100 Ω, 50 4) 100 Ω, 100

**13. **The audio signal used to modulate 30 sin (2 x 106πt) is 15 sin (300πt). Then the depth of the modulation is

1) 10% 2) 50% 3) 75% 4) 100%

**14. **An unregulated input of 10 V is applied across a series combination of a zener diode and a resistor Rs. A regulated voltage Vz = 6 V is required across the load resistor connected across the zener diode. The load current is to be 4 mA. If the zener current is 4 times the load current, then the value of Rs is

1) 50 Ω 2) 100 Ω 3) 150 Ω 4) 200 Ω

**15. **In an n-p-n transistor, the collector current is 9.9 mA. If 99% of the electrons from the emitter reach the collector, find the emitter current and base current?

1) 0.1 mA, 10 mA 2) 10 mA, 0.1 mA 3) 9.9 mA, 0.1 mA 4) 0.1 mA, 9.9 mA

**16. **The electrical conductivity of a semiconductor increases if electromagnetic radiation of wavelength shorter than 2066 nm is incident on it. Then the band gap energy (in eV) for the semiconductor is (approximately)

1) 0.5 2) 0.6 3) 0.7 4) 0.8

**17. **If voltage across the zener diode is 6 V, then the value of the maximum resistance in this condition is

1) 1 kΩ 2) 2 kΩ 3) 3 kΩ 4) 4 kΩ

The voltage drop across the diode D_{2} and the power dissipated by this diode D_{2} are

1) 5 V, 0.7 W 2) 3 V, 0.7 W 3) 5 V, 0 W 4) 0.7 V, 0 W

**19. **In the circuit shown, the current through the battery is (assume all diodes are ideal)

1) 0.5 A 2) 1 A 3) 1.5 A 4) 2 A

**20. **A light emitting diode (LED) has a voltage drop of 2 V across it and a current of 10 mA passes when it operates with a 6V battery through a limiting resistor R. Then the value of R is

1) 400 Ω 2) 4 k Ω 3) 40 k Ω 4) 4 Ω

**21.** If β, RL and r are the ac current gain, load resistance and the input resistance of transistor respectively in CE configuration, the voltage and the power gain respectively are

**22.** The peak voltage in the output of a halfwave diode rectifier fed with a sinusoidal signal without filter is 10 V. Then the dc component of the output voltage is

**23. **A TV tower has a height of 100 m. How much population is covered by the TV broadcost if the average population density around the tower is 1000 km^{-2}. (Radius of the earth = 6.37 x 10^{6} m)

1) 40,000 2) 4 lakh 3) 4 billion 4) 40 lakh

**24. **The electron mobility in N-type Germanium is 3900 cm2V^{-1}s^{-1} and its conductivity is 6.24 mho cm^{-1}. Then the impurity concentration will be

1) 1012 cm^{-3} 2) 1014 cm^{-3} 3) 1015 cm^{-3} 4) 1016 cm^{-3}

**25. **The given electrical network is equal to

1) NOT gate 2) OR gate 3) AND gate 4) NOR gate

**26. **A signal is to be transmitted through a wave of wavelength λ, using a linear antenna. The length l of the antenna and effective power radiated Peff will be given respectively as (k is a constant of proportionality)

1) OR gate 2) NOT gate 3) XOR gate 4) NAND gate

**30. **The figure represents which logic gate?

1) OR 2) AND 3) NOR 4) NAND

**31.** The following configuration of gate is equivalent to

1) OR gate 2) AND gate 3) XOR gate 4) NOR gate

**32. **The output of the following logic circuit is represented as

**Answers: 1-3; 2-4; 3-3; 4-2; 5-1; 6-1; 7-3; 8-3; 9-2; 10-4; 11-1; 12-1; 13-2; 14-4; 15-2; 16-2; 17-4; 18-4; 19-3; 20-1; 21-4; 22-3; 23-4; 24-4; 25-4; 26-2; 27-4; 28-2; 29-1; 30-2; 31-3; 32-4. **