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Q.

Two identical thin rings each of radius ‘R’ are co-axially placed at a distance ‘R’. If the rings have a uniform mass distribution and each has mass m1 and m2 respectively, then the work done in moving a mass ‘m’ from the centre of one ring to that of the other is:

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a

Zero

b

Gmm1−m2(2−1)2R

c

Gm2m1+m2R

d

Gm1m(2+1)m2R

answer is B.

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Detailed Solution

V1=−Gm1R−Gm22R and V2=−Gm2R−Gm12RΔV=V2−V1=−Gm2R−Gm12R+−Gm1R−Gm22R=Gm1−m21R−12RHence W=m(ΔV)=mGm1−m2(2−1)2R

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Two identical thin rings each of radius ‘R’ are co-axially placed at a distance ‘R’. If the rings have a uniform mass distribution and each has mass m1 and m2 respectively, then the work done in moving a mass ‘m’ from the centre of one ring to that of the other is: