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Q.

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 2R from the centre of the sphere. A spherical cavity of radius (R/2) is now made in the sphere as shown in Figure. The sphere with the cavity now applies a gravitational force F2 on the same particle. The ratio (F2/F1) is :

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a

(1/2)

b

(3/4)

c

(7/8)

d

(7/9)

answer is D.

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Detailed Solution

⇒F1=GMm(2R)2,F2=GMm(2R)2−GM8m3R22=7GMm36R2⇒F2F1=7/361/4=79
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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 2R from the centre of the sphere. A spherical cavity of radius (R/2) is now made in the sphere as shown in Figure. The sphere with the cavity now applies a gravitational force F2 on the same particle. The ratio (F2/F1) is :