First slide

Elastic Modulie

Question

Each of three blocks shown in figure has a mass 3kg. The wire connecting, blocks A and B has area of cross-section 0.005 cm² and Young's modulus of elasticity Y = 2×10¹¹N/m². Neglect friction. Find the elastic potential energy stored per unit volume in wire connecting blocks A and B in steady state (in j/m³ take g = 10m/s²)

Moderate

A

500
B

1000
C

2000
D

3000

Solution

$\large 3g-T_1=3a\\T_1-T_2=3a\\T_2=3a\Rightarrow3g=9a\\a=\frac g3 \Rightarrow T_2 = 3\frac{g}{3} = g = 10N\\ \frac {SE}{V}=\frac 12\frac {stress^2}{Y}=\frac 12\frac {10^2}{2(5\times10^{-7})^2\times2\times10^{11}}=1000J/m^3$

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