A body of supercondense material with mass twice the mass of earth but size very small compared to the size of earth starts from rest from `h lt lt R` above the earth's surface. It reaches earth in time

Options

A. `sqrt(2H//g)`
B. `sqrt(H//g)`
C. `sqrt(2H//3g)`
D. `sqrt(4H//3g)`

Answer

C

Explanation

Acceleration of small body w.r.t. earth `=g-(-2g)=3g`
Now from second equation of motion
`H=(1)/(2)(3g)t^(2)impliest=sqrt((2H)/(3g))`
`vecX_(CM)=(2mx_(1)+m(x_(2)))/(2m+m)=(2mH+0)/(2m+m)=(2H)/(3)`
`(H)/(3)=(1)/(2)g t^(2)impliest=sqrt((2H)/(3g))`