A acceleration of moon with respect to earth is 0.0027 `ms^-2` and the acceleration of an apple falling on earth's surface is about `10ms^-2`. Assume that the radius of the moon is one fourth of the earth's radius. If the moon is stopped for an instant and then released, it will fall towards the earth. The initial acceleration of the moon toward the earth will be

Options

A. 0.0027 `ms^(-2)`
B. 5.0 `ms^(-2)`
C. 6.4 `ms^(-2)`
D. 10 `ms^(-2)`

Answer

C

Explanation

just before striking the distance between the centre of earth and moon is `r=R_(e )+(R_(e ))/(4)=(5R_(e ))/(4)`
so acceleartion of moon at this moment is
`g=(GM_(e ))/(5R_(e )//4)^(2)=(gR_(e)^(2))/(25R_(e)^(2))/(25R_(e)^(2))xx16`
`=16/25xx10=6.4 ms^(-2)`