A uniform rectangular parallelopiped of mass m having sides, l, 2l and 4l is placed in turn on each of its three sides on a horizontal surface. What is the potential energy of the parallelopiped in the three positions ? Which position is most stable?

Explanation

When parallelopiped is placed on its small side, its centre of gravity is at height `4l//2=2l` above the horizontal.
`:.` P.E., `U_(1)=mgxx2l=2mgl`
Similarly, when placed on middle side 2l
P.E., `U_(2)=mgxxl=mgl`
And, when placed on large side,
P.E., `U_(3)=mgxx(1)/(2)=mgl//2 ,`
which is minumum. This is the position of stable equilibrium.