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 a cross-sectional area of 0.005 and Young’s modulus . Neglecting friction, the longitudinal strain on wire B is _____ . (Take g = 10 ).

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Solution

Q.
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 a cross-sectional area of 0.005 ${cm}^{2}$ and Young’s modulus $2 \times 10^{11}$ $N m^{2}$ . Neglecting friction, the longitudinal strain on wire B is _____ $\times 10^{- 4}$ . (Take g = 10 $m / s^{2}$ ). [2024]

Ans.
(2)

$3 g = (3 + 3 + 3) a \Rightarrow a = \frac{3}{9} g = \frac{1}{3} g$

$Now, 3 g - T = 3 a$

$\Rightarrow T = 3 (g - a) = 3 (g - \frac{g}{3}) = 2 g = 20 N$

$Y = \frac{longitudinal stress}{longitudinal strain}$

$longitudinal strain = \frac{longitudinal stress}{Y}$

$= \frac{T}{A Y} = \frac{20}{5 \times 10^{- 7} \times 2 \times 10^{11}} = 2 \times 10^{- 4}$

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