Mechanical Properties of Solids

JEE Main level, single correct, medium

63 of 118

Question 63 of 118

If Y,KY,K and η\eta are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

Show answer and solution

Answer: (C) K=Yη9η−3YNm−2K=\dfrac{Y\eta }{9\eta -3Y}N{m}^{-2}

Y−Y-Young's modulus, K−K-Bulk modulus, η−\eta -modulus of rigidity
We know that,
Y=3k(1−2σ)Y=3k\left(1-2\sigma \right)
⇒σ=12(1−Y3k)...(1)\Rightarrow \sigma =\dfrac{1}{2}\left(1-\dfrac{Y}{3k}\right)...\left(1\right)
⇒Y=2η(1+σ)\Rightarrow Y=2\eta \left(1+\sigma \right)⇒σ=Y2η−1...(2)\Rightarrow \sigma =\dfrac{Y}{2\eta }-1...\left(2\right)
From the equation (1)\left(1\right) and the equation (2)\left(2\right)
12(1−Y3k)=Y2η−1\dfrac{1}{2}\left(1-\dfrac{Y}{3k}\right)=\dfrac{Y}{2\eta }-1
⇒1−Y3k=Yη−2\Rightarrow 1-\dfrac{Y}{3k}=\dfrac{Y}{\eta }-2⇒Y3k=3−Yn\Rightarrow \dfrac{Y}{3k}=3-\dfrac{Y}{n}⇒Y3k=3η−Yη\Rightarrow \dfrac{Y}{3k}=\dfrac{3\eta -Y}{\eta }
⇒ηY3k=3η−Y\Rightarrow \dfrac{\eta Y}{3k}=3\eta -Y⇒k=ηY9η−3YNm−2\Rightarrow k=\dfrac{\eta Y}{9\eta -3Y}N{m}^{-2}.

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Elasticity: stress, strain and Young’s modulus simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Mechanical Properties of Solids (Young's Modulus and Breaking Stres), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.