JEE PYQ: Properties Of Matter Question 17
Question 17 - 2019 (09 Jan 2019 Shift 1)
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 $\alpha$/°C. 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:
(1) $\frac{F}{A,\alpha,\Delta T}$
(2) $\frac{F}{A,\alpha,(\Delta T - 273)}$
(3) $\frac{F}{2A,\alpha,\Delta T}$
(4) $\frac{2F}{A,\alpha,\Delta T}$
Show Answer
Answer: (1)
Solution
$Y = \frac{\text{stress}}{\text{strain}} = \frac{F/A}{\Delta l/l}$. Since $\frac{\Delta l}{l} = \alpha \Delta T$, we get $Y = \frac{F}{A\alpha\Delta T}$
BETA
