A brass rod of cross-sectional area 1 ,c m^2 and length 0.2 , m i… - Vidyadip

MCQ

A brass rod of cross-sectional area $1\,c{m^2}$ and length $0.2\, m$ is compressed lengthwise by a weight of $5\, kg$. If Young's modulus of elasticity of brass is $1 \times {10^{11}}\,N/{m^2}$ and $g = 10\,m/{\sec ^2}$, then increase in the energy of the rod will be

A
${10^{ - 5}}\,J$
✓
$2.5 \times {10^{ - 5}}\,J$
C
$5 \times {10^{ - 5}}\,J$
D
$2.5 \times {10^{ - 4}}$ $J$

✓

Answer

Correct option: B.

$2.5 \times {10^{ - 5}}\,J$

b
(b) $U = \frac{1}{2} \times \frac{{{{{\rm{(stress)}}}^{\rm{2}}}}}{Y} \times {\rm{volume}}$$=$ $\frac{1}{2} \times \frac{{{F^2} \times A \times L}}{{{A^2} \times Y}}$

$=$$\frac{1}{2} \times \frac{{{F^2}L}}{{AY}} = \frac{1}{2} \times \frac{{{{(50)}^2} \times 0.2}}{{1 \times {{10}^{ - 4}} \times 1 \times {{10}^{11}}}}$$=$ $2.5 \times {10^{ - 5}}J$

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