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, so that each block hangs freely on its own side of the pulley. The radius of the wire is 4.0×10⁻⁵ m and Young's modulus of the metal is 2.0×10¹¹ N m⁻². The longitudinal strain develope…

Question

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, so that each block hangs freely on its own side of the pulley. The radius of the wire is 4.0×10⁻⁵ m and Young's modulus of the metal is 2.0×10¹¹ N m⁻². The longitudinal strain developed in the wire is 1/(απ). The value of α is . [Use g=10 m s⁻²]

Accepted Answer

12. Given: m₁=2 kg, m₂=4 kg, r=4.0×10⁻⁵ m, Y=2.0×10¹¹ N m⁻². The wire over a smooth pulley carries one tension throughout, T=(2m₁m₂g)/(m₁+m₂)=(2×2×4×10)/6=(80)/3 N. A=π r²=π(4.0×10⁻⁵)²=1.6×10⁻⁹π m², so AY=1.6×10⁻⁹π×2.0×10¹¹=320π N. Strain =T/(AY)=(80)/(3×320π)=1/(12π). Comparing with 1/(απ) gives α=12.

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