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Each of three blocks P, Q and R shown in the figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area $0.005\ \text{cm}^2$ and Young's modulus $2 \times 10^{11}\ \text{Nm}^{-2}$ . Neglecting friction, the longitudinal strain on wire B is ______ $\times 10^{-4}$ . (Take $g = 10\ \text{m/s}^2$ )

Blocks P, Q, R connected by wires A and B hanging from a support with R at the bottom

![Blocks P, Q, R connected by wires A and B hanging from a support with R at the bottom](https://www.edvaya.com/jee/physics/q11-blocks-pqr-wires-ab-2024.png) A). 1 B). 2 C). 3 D). 4

Edvaya · Accepted Answer

The correct answer is 3. Assuming the standard configuration where wire B connects block Q to block R (with R hanging at the bottom).
The tension in wire B supports only block R:
$T_B = m_R 	imes g = 3 	imes 10 = 30\ 	ext{N}$
Cross-sectional area: $A = 0.005\ 	ext{cm}^2 = 0.005 	imes 10^{-4}\ 	ext{m}^2 = 5 	imes 10^{-7}\ 	ext{m}^2$
Longitudinal strain:
$\varepsilon = \dfrac{T_B}{Y 	imes A} = \dfrac{30}{2 	imes 10^{11} 	imes 5 	imes 10^{-7}}$ 
$= \dfrac{30}{10^5} = 3 	imes 10^{-4}$
Therefore, the required value is 3.

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Physics > Properties Of Bulk Matter > Mechanical Properties Of Solids

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