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Mechanical Properties of Solids · Question 18

JEE Main 2025 (Online) 4th April Evening ShiftMCQEasy📈 Topic in 10% papers+4−1
1

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 105 N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement of the rod axis from its original position would be : (shear modulus, G = 1010 N/m2)

  1. 1/160
  2. 1/2
  3. 1/4
  4. 1/40

Answer

(1) 1/160

Solution

Area of the top face on which the shear force acts:

A = r2 = (0.04)2 = 1.6 10-3 m2

Shear modulus G = F/A

= FAG = 1051.6 10-3 1010

= 1160 rad

Answer: (1)

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2

A steel wire of length 2 m and Young's modulus 2.0 1011 N m-2 is stretched by a force. If Poisson's ratio and transverse strain for the wire are 0.2 and 10-3 respectively, then the elastic potential energy density of the wire is 105 (in SI units).

JEE Main 2025 (Online) 2nd April Morning Shift
3

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is m.

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4

The fractional compression ( VV ) of water at the depth of 2.5 km below the sea level is %. Given, the Bulk modulus of water = 2 109 N m-2, density of water = 103 kg m-3, acceleration due to gravity g = 10 m s-2.

  1. 1.0
  2. 1.25
  3. 1.75
  4. 1.5
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5

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of 7 106 Pa, would be mm3. (Given bulk modulus of copper = 1.4 1011 N m-2)

JEE Main 2025 (Online) 28th January Evening Shift

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