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Mechanical Properties of Solids · Question 19

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1

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).

Answer

25

Solution

Poisson's ratio: = transverse strainlongitudinal strain

longitudinal strain = 10-30.2 = 5 10-3

Energy density: u = 12Y(strain)2

= 12 2 1011 (5 10-3)2

= 25 105 J m-3

Answer: 25

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2

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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3

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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4

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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