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Q.

A uniform rod of mass m, length  l is freely suspended vertically from a fixed horizontal support.( ρ = density of the rod, Y = Young’s modulus of the rod, A = area of cross section of the rod). In this situation mark out the correct statement(s)

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a

The elongation of the rod is  mgl2AY

b

The elongation of the rod is  ρgl22Y

c

Elastic potential energy stored in the rod is 16  m2g2lAY

d

Elastic potential energy stored in the rod is 16  ρ2g2l3AY

answer is A.

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Detailed Solution

e=∫0lmg ydylAY=mgl2AYU=∫0l12m2g2l2AYy2dy=m2g2l6AY
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