Two point masses `A` of mass `M` and `B` of mass of `4M` are fixed at the ends of a rod of length `l` and of negligible mass. The rod is set rotation about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass `A` is at

Options

A. `2/5l`
B. `8/5l`
C. `4/5l`
D. `l/5`

Answer

C

Explanation

`W=1/2 Iomega^(2)`
Let `x` is the distance of `CM` from `A`
`I=Mx^(2)+4Mxx2(l-x)xx(-1)=2Mx-8 Ml`
`(dI)/(dx)=10-8Ml=0, x=4/5l`