Q 11-08-045JEE MainJEE Main 2024 (30 Jan, Shift 1)Medium
Each of three blocks $P$, $Q$ and $R$ shown in the figure has a mass of $3\ \text{kg}$. Each of the wires $A$ and $B$ has cross-sectional area $0.005\ \text{cm}^2$ and Young's modulus $2\times10^{11}\ \text{N m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is ______ $\times10^{-4}$. (Take $g = 10\ \text{m s}^{-2}$)
Numerical value type. Enter your answer.
Answer: 2
The whole system (9 kg) is pulled by the weight of R:
$$a = \frac{3\times10}{9} = \frac{10}{3}\ \text{m s}^{-2}$$
Wire B pulls both P and Q: $T_B = 6\times\dfrac{10}{3} = 20\ \text{N}$.
$$\text{strain} = \frac{T_B}{AY} = \frac{20}{(0.005\times10^{-4})(2\times10^{11})} = \frac{20}{10^5} = 2\times10^{-4}$$
Solution by Sreeraj P, M.Sc Physics