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Q.

A mass m is placed at point P which lies on the axis of a ring of mass M and radius R at a distance R from its centre. The gravitational force on mass m is

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a

GMm2R2

b

GMm2R2

c

GMm22R2

d

GMm4R2

answer is C.

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Detailed Solution

The situation is as shown in the figure.Gravitational force on an object of mass m at point P at distance d from centre O lying on the axis of the circular ring of radius R and mass M is given byF=GMmdR2+d23/2When d = R, then F=GMmRR2+R23/2=GMmR2R23/2=GMmR23/2R3=GMm22R2
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A mass m is placed at point P which lies on the axis of a ring of mass M and radius R at a distance R from its centre. The gravitational force on mass m is