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A uniform rod of mass M and length L is ...

A uniform rod of mass M and length L is held vertically upright on a horizontal surface as shown in figure. Assuming zero potential energy at the base of the rod, determine the potential energy of the rod.

Text Solution

Verified by Experts

Choose a small element of length `dy`, then
mass of the element `dm = ((m)/(L)) dy`.
The potential energy of the element `dU = (dm)g(y)`
Potential energy of the entire rod
`U = underset(0) overset(L)int (dm) gy = underset(0) overset(L)int ((m)/(L)) (dy).gy = (m)/(L) g underset(0) overset(L)int ydy`
`U =(m)/(L) g((y^(2))/(2))_(0)^(L) = (mgL)/(2)`.
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