Q.

Two identical thin rings each of radius R are coaxially placed at a distance R. If the rings have a uniform mass distribution and each has masses 2m and 4m respectively, then the work done in moving a mass m from centre of one ring to that of the other is

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a

zero

b

2Gm2R(1-2)

c

Gm22R(2-1)

d

Gm22R

answer is B.

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Detailed Solution

Work done, W=U2-U1=mv2-mv1=m-Gm2R-Gm12R--Gm1R-Gm22R=Gmm1-m22R(2-1)=2Gm2R(1-2)
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Two identical thin rings each of radius R are coaxially placed at a distance R. If the rings have a uniform mass distribution and each has masses 2m and 4m respectively, then the work done in moving a mass m from centre of one ring to that of the other is