R4RIN – MCQs, Mock Tests | IIT JEE IIT JEE Elasticity

A load suspended by a massless spring produces an extension of x cm in equilibrium. When it is cut into two unequal parts the same load produces an extension of 7.5 cm when suspended by the large part of length 60 cm. When it is suspended by the smaller part the extension is 5.0 cm. then:

1. x = 12.5
2. x = 3.0
3. the length of the original spring is 90 cm
4. the length of the original spring is 80 cm

✅ Correct Answer: 1

A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of same length and radius 2R will be

1. F / 2
2. 2F
3. 4F
4. F / 4

✅ Correct Answer: 3

When a weight of 5 kg is suspended from a copper wire of length 30 m and radius 0.5 mm the length of the wire increases by 2.4 cm. If the radius is doubled the extension produced is:

1. 1.2 cm
2. 0.6 cm
3. 0.3 cm
4. 0.15 cm

✅ Correct Answer: 2

For gases:

1. isothermal elasticity is greater than adiabatic elasticity
2. adiabatic elasticity is greater than isothermal elasticity
3. both the elasticities are equal
4. none of the above

✅ Correct Answer: 2

On what factor should the coefficient of restitution depend when two bodies having masses m and M (m < M) collide with each other?

1. Coefficient of restitution depends upon Youngs modulus of elasticity of heavier body only
2. Coefficient of restitution depends upon Youngs modulus of elasticity of lighter body only
3. Coefficient of restitution depends upon Youngs modulus of elasticity of both the bodies
4. Coefficient of restitution depends upon Nature of collision (wheather it is head on or oblique)

✅ Correct Answer: 3

A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is:

1. 0.2 J
2. 10 J
3. 20 J
4. 0.1 J

✅ Correct Answer: 4

Youngs modulus is defined for:

1. solid
2. liquid
3. gas
4. all of these

✅ Correct Answer: 1

The longitudinal extension of any elastic material is very small. In order to have an appreciable change the material must be in the form of:

1. thin block of any cross-section
2. thick block of any cross-section
3. long thin wire
4. short thin wire

✅ Correct Answer: 3

Youngs modulus for perfectly inelastic body is:

1. finite
2. one
3. zero
4. infinity

✅ Correct Answer: 3

Which of the following substances has the highest value of the Youngs modulus?

1. Steel
2. Rubber
3. Wood
4. Plastic

✅ Correct Answer: 4

A wire is stretched 1 mm by a force of 1 kN. How far would a wire of the same material and length but of four times that diameter be stretched by the same force ?

1. 1 / 2 mm
2. 1 / 4 mm
3. 1 / 8 mm
4. 1 / 16 mm

✅ Correct Answer: 4

When a rubber cord is stretched the change in volume with respect to change in its linear dimensions is negligible. The Poisson s ratio for rubber is

1. 1
2. 0.25
3. 0.5
4. 0.75

✅ Correct Answer: 3

When a certain weight is suspended from a long uniform wire its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one the increase in length will be

1. 0.5 cm
2. 2 cm
3. 4 cm
4. 8 cm

✅ Correct Answer: 3

Four wires of the same material are stretched by the same load. The dimensions of the wires are as given below. The one which has the maximum elongation is of:

1. diameter 1 mm and length 1 m
2. diameter 2 mm and length 2 m
3. diameter 0.5 mm and length 0.5 m
4. diameter 3 mm and length 3 m

✅ Correct Answer: 3

When the intermolecular distance decreases due to compressive force there is:

1. zero resultant force between molecules
2. repulsive force between molecules
3. attractive force between molecules
4. no force between molecules

✅ Correct Answer: 2

A string 1 mm in diameter breaks if the tension in it exceeds 80 N. The maximum tension that may be given to a similar string of diameter 2 mm is

1. 40 N
2. 80 N
3. 320 N
4. 1640 N

✅ Correct Answer: 3

A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends the elongation of the wire will be (in mm):

1. 1
2. 21
3. zero
4. 1/2.

✅ Correct Answer: 1

A wire can sustain a weight of 10 kg before breaking. If the wire is cut into two equal parts then each part can sustain a weight of

1. 2.5 kg
2. 5 kg
3. 10 kg
4. 15 kg

✅ Correct Answer: 3

The length of an elastic string is a metre when the tension is 4 N and b metre when the tension is 5 N. The length in metres when the tension is 9 N is:

1. 4a ? 5b
2. 5b ? 4a
3. 9b ? 9a
4. a + b

✅ Correct Answer: 2

A spring of constant K is cut into parts of length in the ration 1 : 2. The spring constant of larger one is

1. K / 2
2. K / 3
3. 2K / 3
4. 3K / 2

✅ Correct Answer: 1

Two bars A and B of circular cross-section and of same volume and made of the same material are subjected to tension. If the diameter of A is half that of B and if the force applied to both the rods is the same and it is in the elastic limit the ratio of extension of A to that of B will be842

1. 16
2. 8
3. 4
4. 1

✅ Correct Answer: 1

What happen to the elastic property of a substance after annealing (cooling slowly after heating)?

1. Increases
2. Decreases
3. Remains as such
4. Becomes zero

✅ Correct Answer: 2

Two wires of the same material and radius but having length in the ratio of 1 : 2 are stretched with the same force. The ratio of the work done in two cases is

1. 1:02
2. 2:01
3. 1:03
4. 1:08

✅ Correct Answer: 1

Two wires of the same material and length are stretched by the same force. Their masses are in the ratio 3:2 their elongations are in the ratio:

1. 3:02
2. 9:04
3. 2:03
4. 4:09

✅ Correct Answer: 3

The property due to which a material can be hammered into thin sheet is called:

1. ductility
2. malleability
3. brittleness
4. elasticity

✅ Correct Answer: 2

The modulus of elasticity is dimensionally equivalent to:

1. surface tension
2. stress
3. strain
4. none of these

✅ Correct Answer: 2

The Youngs modulus of a wire is numerically equal to the stress which will:

1. not change the length of the wire
2. double the length of the wire
3. increase the length by 50%
4. change the radius of the wire to half

✅ Correct Answer: 1

If a metal wire of length L having area of cross-section A and Youngs modulus Y behaves as a spring of spring constant k. The value of k is:

1. YA/L
2. YA/2L
3. 2YA/L
4. YL/A

✅ Correct Answer: 1

You are given three wires A B and C of the same length and cross-section. They are each stretched by applying the same force to the ends. The wire A is stretched least and comes back to its original length when the stretching force is removed. The wire B is stretched more than A and also comes back to its original length when the stretching force is removed. The wire C is stretched most and remains stretched even when stretching force is removed. The greatest Young s modulus of elasticity is possessed by the material of wireABC

1. A
2. B
3. C
4. Data is not sufficient

✅ Correct Answer: 1

The length of a wire is increased by 1 mm on the application of given load. In a wire of the same material but of length and radius twice that of the first on the application of the same load extension is4 mm

1. 0.25 mm
2. 0.5 mm
3. 2 mm
4. 1 mm

✅ Correct Answer: 2

Two wires of the same length and same material but radii in the ratio of 1 : 2 are stretched by unequal forces to produce equal elongation. The ratio of the two forces is

1. 1:01
2. 1:02
3. 1:03
4. 1:04

✅ Correct Answer: 4

The dimensions of four wire of the same material are given below. In which wire the increase in length will be maximum ?

1. Length 100 cm Diameter 1 mm
2. Length 200 cm Diameter 2 mm
3. Length 300 cm Diameter 3 mm
4. Length 50 cm Diameter 0.5 mm.

✅ Correct Answer: 4

Two wires of the same material and length are stretched by the same force. Their masses are in the ratio 3 : 2. Their elongations are in the ratio

1. 3:02
2. 9:04
3. 2:03
4. 4:09

✅ Correct Answer: 3

If the work done in stretching a wire by 1 mm is 2 J the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by 1 mm is

1. 1 / J
2. 4 J
3. 8 J
4. 16 J

✅ Correct Answer: 4

Two identical wires are suspended from the same rigid support but one is of copper and the other is of iron. Young s modulus of iron is thrice that of copper. The weights to be added on copper and iron wires so that the ends are on the same level must be in the ratio of

1. 1:03
2. 2:01
3. 3:01
4. 4:01

✅ Correct Answer: 1

A uniform wire fixed at its upper end hangs vertically and supports a weight at its lower end. If its radius is r its length L and Young s modulus for the material of the wire is E the extension is (1) directly proportional to E(2) inversely proportional to r.(3) directly proportional to L

1. if 1 2 3 are correct
2. if 1 2 are correct
3. if 2 3 are correct
4. if 3 only is correct

✅ Correct Answer: 4

A force F is required to break a wire or length l and radius r. What force is required to break a wire of the same material having twice the length and six times the radius ?

1. F
2. 3 F
3. 9 F
4. 36 F

✅ Correct Answer: 3

A cube of aluminium of sides 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

1. 0.02
2. 0.1
3. 0.005
4. 0.002

✅ Correct Answer: 4

The length of an elastic string is a metre when the tension is 4 N and b metre when the tension is 5 N. The length in metre when the tension is 9 N is

1. 5b - 4a
2. 4a - 5b
3. a + b
4. b - a

✅ Correct Answer: 1

A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radius. The shear strain developed will be

1. 0.002
2. 0.004
3. 0.008
4. 0.016

✅ Correct Answer: 2

A helical spring extends 40 mm when stretched by a force of 10 N and for tensions up to this value the extension is proportional to the stretching force. Two such springs are joined end to-end and the double-length spring is stretched 40 mm beyond its natural length. The total strain energy in J stored in the double spring is

1. 0.05
2. 0.1
3. 0.2
4. 0.4

✅ Correct Answer: 2

Three wires PQ and R of the same material and length have radii 0.1 cm 0.2 cm and 0.3 cm respectively. Which wire has the highest value of Young s modulus of elasticity ?PQR

1. P
2. Q
3. R
4. All have the same value

✅ Correct Answer: 4

The increase in length on stretching a wire is 0.05%. If its Poisson s ratio is 0.4 the diameter is reduced by

1. 0.01%
2. 0.02%
3. 0.03%
4. 0.04%

✅ Correct Answer: 2

A piece of copper wire has twice the radius of a piece of steel wire. The Young s modulus for steel is twice that for the copper. One end of the copper wire is joined to one end of the steel wire so that both can be subjected to the same longitudinal force. By what fraction of its length of the copper has increased by 1% ?

1. 1%
2. 2%
3. 2.50%
4. 3%

✅ Correct Answer: 2

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F its length increases by l . Another wire of the same material of length 4 L and radius 4r is pulled by a force 4F. The increase in length will be

1. l / 2
2. l
3. 2l
4. 4l

✅ Correct Answer: 2

A wire extends by 1 mm when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be

1. 8
2. 4
3. 2
4. 1

✅ Correct Answer: 1

For a given material the Young s modulus is 2.4 times that of modulus of rigidity. Its Poisson s ratio is

1. 0.1
2. 0.2
3. 0.3
4. 0.4

✅ Correct Answer: 2

Two wires of the same material and same are stretched by the same force. Their lengths are in the ratio 2 : 3. Their elongations are in the ratio

1. 3:02
2. 2:03
3. 4:09
4. 9:04

✅ Correct Answer: 3

When a weight of 5 kg is suspended from a copper wire of length 30 m and diameter. 0.5 the length of the wire increases by 2.4 cm. If the diameter is doubled the extension produced is

1. 1.2 cm
2. 0.6 cm
3. 0.3 cm
4. 0.15 cm

✅ Correct Answer: 2

When a 4 kg mass is hung vertically on a light spring that obeys Hooke s law the spring stretches by 2 cm. The work required to be done by an external agent in stretching this spring by 5 cm will be

1. 4.9 J
2. 2.45 J
3. 0.495 J
4. 0.245 J

✅ Correct Answer: 2