What impulse need to be given to a body of mass `m`, released from the surface of earth along a straight tunnel passing through centre of earth, at the centre of earth, to bring it to rest. (Mass of earth M, radius of earth R)

Options

A. `msqrt((GM)/(R))`
B. `sqrt((GMm)/(R))`
C. `msqrt((GM)/(2R))`
D. zero

Answer

A

Explanation

Conservation of mechanical energy gives,
`(1)/(2)mv^(2)=m[-(GM)/(R)+(3GM)/(2R)]=(GMm)/(2R)`
`because` increase in KE = decrease in PE) or `v = sqrt((GM)/(R))`
Momentum, `mv = m sqrt((GM)/(R))`
`:.` Impulse required `= sqrt((GM)/(R))`.