In a solid sphere of radius ‘R’ and density ‘ ρ ’ there is a spherical cavity of radius R/4 as shown in figure. A particle of mass ‘m’ is released from rest from point ‘B’ (inside the cavity). Find out Velocity (in mm/sec.) of the particle at the instant when it strikes the cavity (R = 3m, ρ = 
kg/m 3 , G = 
Nm 2 kg –2 )
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
v = 
= 2mm/sec.
Sol- The gravitation field is uniform inside the cavity and is directed along 
. Hence the particle will
strike at A.
The gravitational field at any point P inside cavity.
| 
| = G ρ 
– 
G ρ 
= 
Gy 
= 
G ρ R
Total work done = m | 
|. 
= m. 
G ρ R. 
Applying work - energy theorem
Work done by all force = Change in kinetic energy
m. 
G ρ R. 
= 
mv 2
v = 
= 2mm/sec
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