Question

Two point masses of 0.3 kg and 0.7 kg are fixed at the end of rod of length 1.4m and of negligible mass. The rod is set rotating about an axis perpendicular to it's length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of?

Answer 1

As it is easiest to rotate a body about its center of mass .

Answer 2

Work-energy theorem, W=  1/2 Iw          

w  is constant

So required work done to be minimum implies that I must be minimum.

I=0.3(x ^2 )+0.7(1.4−x)  ^2  

For I to be minimum, dI/dx=0

⟹0.3×2(x)−0.7×2(1.4−x)=0

⟹x=0.98m

∴ x is 0.98 m from 0.3 kg mass