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Mechanical Properties of Solids · Question 7

JEE Main 2026 (Online) 5th April Evening ShiftNumericalMedium📈 Topic in 6% papers+4
1

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is 600 10-6 m3. The elastic potential energy stored in the wire in stretched condition would be J. (Given Young modulus of copper = 1.1 1011 N/m2)

Answer

33

Solution

Strain = ll= 3 10-33=10-3

Energy density u= 12 = 12Y(strain)2

U= 12Y(strain)2 V

= 12 1.1 1011 (10-3)2 600 10-6

=0.55 105 600 10-6

U=33 J

Answer: 33

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2

The increase in the pressure required to decrease the volume ( V) of water is 6.3 107 N/m2. The percentage decrease in the volume is . (Bulk modulus of water =2.1 109 N/m2.)

  1. 2 %
  2. 3 %
  3. 6 %
  4. 4 %
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3

A string A of length 0.314 m and Young's modulus 2 1010 N/m2 is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is mm. (radius of both the strings is 0.2 mm and acceleration due to gravity = 10 m/s2) (Mass of both strings is to be neglected as compared to the mass of load)

  1. 3
  2. 2
  3. 1.9
  4. 1
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4

A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2M is suspended at the bottom of the first block using a string B. The area of cross sections of strings A and B are same. The ratio of lengths of strings of A to B is 2 and the ratio of their Young's moduli (YA/YB ) is 0.5. The ratio of elongations in A to B is .

  1. 1
  2. 4
  3. 8
  4. 6
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5

A uniform wire of length l of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at l3 distance from the top is ( WA+ 2 wA ), where A is the cross sectional area of the wire. The value of is .

JEE Main 2026 (Online) 2nd April Morning Shift
6

Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 10-5 m2 and 4.5 10-5 m2, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x is

  1. 2
  2. 1
  3. 4
  4. 5
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7

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus ? [figure]

  1. B
  2. A
  3. D
  4. C
JEE Main 2026 (Online) 23rd January Morning Shift
8

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is P 1011 N m-2, where the value of P is: (Take g = 3 m/s2)

  1. 2.5
  2. 25
  3. 10
  4. 5
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9

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm3. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was litre. (Take 1 atm = 105 Pa)

JEE Main 2025 (Online) 8th April Evening Shift
10

Two wires A and B are made of same material having ratio of lengths LALB = 13 and their diameters ratio dAdB = 2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

  1. 3 : 4
  2. 1 : 12
  3. 1 : 3
  4. 1 : 6
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11

Two slabs with square cross section of different materials (1, 2) with equal sides (l) and thickness d1 and d2 such that d2 = 2d1 and l > d2. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is 2 = 2 1. If the shear modulus of material 1 is 4 109 N/m2, then shear modulus of material 2 is x 109 N/m2, where value of x is .

JEE Main 2025 (Online) 4th April Morning Shift

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