Two point masses A of mass M and B of mass 4 M are fixed at the ends of a rod of length land of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum, then the distance ofaxis 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=1/2Iomega^2`
Let x is the distance of CM from A.,` I=Mx^2 + 4M(l -x)^2` and if I is minimum, W will be minimum.
`(dI)/(dx)=2Mx+4Mxx2(l-x)xx-1=2Mx-8M(l-x)`
`(dI)/(dx)=10 Mx-8Ml :. 10Mx - 8Ml =0 , x =4/5l`