Question

A copper rod of length l and radius r is suspended from the ceiling by one of its ends. Find the elastic potential energy stored in the rod by its ow weight

Answer 1

Potential energy stored in the copper rod = πr^3gL^2.

Explanation:

According to Hook's law:      

mg/πr^2 = Y×Δl/L

OR    

mgL=Y×πr^2×Δl  .......(1)

OR

πr^2L× r × gL= Y × πr^2 × Δl

Or Δl=grL^2/Y .......(2)

Putting this value of Δl in equation (1) we get.

mgL= Y×πr^2×grL^2/Y = πr^3gL^2

Therefore potential energy stored in the copper rod = πr^3gL^2.

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