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Two point masses of 0.3 kg and 0.7kg are...

Two point masses of 0.3 kg and 0.7kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its 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

A

0.42 m from the mass of 0.3 kg

B

0.70 m from the mass of 0.7 kg

C

0.98 m from the mass of 0.3 kg

D

0.98 m from the mass of 0.7 kg

Text Solution

Verified by Experts

The correct Answer is:
C
The moment of inertia of the system about axis of rotation O is
`I=I_(1) + I_(2)`
`=0.3 x^(2) + 0.7(1.4 -x)^(2)`
`=0.3x^(2) + 0.7 (1.96 +x^(2) -2.8x)`
`=x^(2) + 1.372 -1.96x`

The work done in rotating the rod is converted into its rotational kinetic energy.
`therefore W=1/2 Iomega^(2) =1/2[x^(2) + 1.372 -1.96x]omega^(2)`
For work done to be minimum.
`(dW)/(dx)=0 rArr 2x-1.96 =0 rArr x=(1.96)/2 = 0.98 m`
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