A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F1 on a particle placed at a distance 3R from the centre of the sphere. A spherical cavity of radius R2 is now made in the sphere, as shown in the figure. The sphere with cavity now applies a gravitational force F2 on the same particle. The ratio F2F1 is
4150
2225
325
950
A
4150
B
950
C
325
D
2225
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Solution
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From super position
principle ,
F1=Fr+Fc
Here Fr= force
due to remaining part =F2
Fc=
force due to mass on the cavity
F1=GMm9R2
Fc=G(M8)m(52R)2=GMm50R2
=≻F2=F1−Fc=GMm9R2−GMm50R2=41GMm450R2
⇒F2F1=4150
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