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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Mechanical Properties of Solids

NTA Abhyas 2020 · Physics · Mechanical Properties of Solids

The pressure applied from all directions on a cube is p. How much...

The pressure applied from all directions on a cube is p.p. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is β\beta and the coefficient of volume expansion is α.\alpha.

Options

  1. Apαβ\dfrac{p}{\alpha\beta}
  2. Bpαβ\dfrac{p\alpha}{\beta}
  3. Cpβα\dfrac{p\beta}{\alpha}
  4. Dαβp\dfrac{\alpha\beta}{p}

Correct answer

A. pαβ\dfrac{p}{\alpha\beta}

Step-by-step solution

If coefficient of volume expansion is α\alpha and rise in temperature is ∆θ,∆ \theta, then ∆V=Vα∆θ∆ V = V\alpha ∆ \theta

⇒∆VV=α∆θ⇒ \dfrac{∆ V}{V} = \alpha ∆ \theta

∴∴ Volume elasticity, β=p∆V/V\beta = \dfrac{p}{∆ V / V}

=pα∆θ= \dfrac{p}{\alpha ∆ \theta}

⇒∆θ=pαβ⇒ ∆ \theta = \dfrac{p}{\alpha\beta}
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