A brass rod of cross-sectional area 1 cm 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 - 1011 N - m 2 and g-10 m - sec 2- then increase in the energy of the rod will beA- 10-5 JB- 2-5 - 10-5 JC- 2-5 - 10-4 JD- 5 - 10-5 J

The correct option is B U=1/2×(stress)^2/Y× volume =1/2×F^2 × A × L/A^2 × Y = 1/2×F^2 L/AY = 1/2×(50)^2 × 0.2/1 × 10^ 4× 1 ×10^11= 2.5 × 10^ 5 J ...

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Standard XII

Physics

Stress-Strain Graph

A brass rod o...

Question

A brass rod of cross-sectional area 1 and length 0.2 m is compressed lengthwise by a weight of 5 kg. If Young's modulus of elasticity of brass is and , then increase in the energy of the rod will be

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Solution

The correct option is B

$U = \frac{1}{2} \times \frac{(s t r e s s)^{2}}{Y} \times v o l u m e = \frac{1}{2} \times \frac{F^{2} \times A \times L}{A^{2} \times Y} = \frac{1}{2} \times \frac{F^{2} L}{A Y} = \frac{1}{2} \times \frac{(50)^{2} \times 0.2}{1 \times 10^{- 4} \times 1 \times 10^{11}} = 2.5 \times 10^{- 5} J$

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A brass rod of cross-sectional area 1 and length 0.2 m is compressed lengthwise by a weight of 5 kg. If Young's modulus of elasticity of brass is and , then increase in the energy of the rod will be

The correct option is B U=12×(stress)2Y×volume=12×F2×A×LA2×Y=12×F2LAY=12×(50)2×0.21×10−4×1×1011=2.5×10−5J