A rod, of length L at room temperature and uniform area of cross… | JEE Main 2019 (9 Jan, Shift 1)

Q61JEE Main 2019 · 9 JAN · SHIFT 1Medium

Thermometry & Thermal Expansion

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $\alpha$ /oC. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $\Delta$ T K. Young's modulus, Y, for this metal is:

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Answer: (a)

Prevented expansion gives thermal strain $\alpha\Delta T$ .
$\dfrac{F}{A} = Y\alpha\Delta T$ (a change of $\Delta T$ is the same in K and $^\circ$ C).
$Y = \dfrac{F}{A\alpha\Delta T}$ , answer (a).

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