A hollow spherical shell is compressed to half its radius. The gravitational potential at the centre

Options

A. increases
B. decreases
C. remains same
D. during the compression increases then returns at the previous value

Answer

B

Explanation

`v'` speed at minimum distance
conserve angular momentum
`m_(2)v_(0)(2R)=mv'R` ..(i)
conerve TME
`(1)/(2)mv_(0)^(2)+((-MGm)/(2R))=(1)/(2)m(v')^(2)+((-GMm)/(R))` ..(ii)
`v''=` speed of satellite in circular orbit
`(GMm)/((2R)^(2))=(m(v'')^(2))/((2R))` ..(iii)