Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in the figure. The radius of the wire is m and Young’s modulus of the metal is . The longitudinal strain developed in the wire is . The value of is

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Solution

Q.
Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in the figure. The radius of the wire is $4.0 \times 10^{- 5}$ m and Young’s modulus of the metal is $2.0 \times 10^{11}$ $N / m^{2}$ . The longitudinal strain developed in the wire is $\frac{1}{α π}$ . The value of $α$ is _______ .

[Use g = 10 $m / s^{2}$ ] [2024]

Ans.
(12)

$T = (\frac{2 m_{1} m_{2}}{m_{1} + m_{2}}) g = \frac{80}{3} N$

$A = π r^{2} = 16 π \times 10^{- 10} m^{2}$

$Strain = \frac{Δ ℓ}{ℓ} = \frac{F}{A Y} = \frac{T}{A Y}$

$= \frac{\frac{80}{3}}{16 π \times 10^{- 10} \times 2 \times 10^{11}} = \frac{1}{12 π}$

$α = 12$

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