A satellite is moving with a constant speed 'V' in a circular orbit about the earth. An object of mass 'm' is ejected from the satellite such that it just escapes form the gravitational pull of the earth. At the tme of its ejection, the kinetic energy of the object is

Options

A. `(1)/(2)mv^(2)`
B. `mv^(2)`
C. `(3)/(2)mv^(2)`
D. `2mv^(2)`

Answer

B

Explanation

Trhe orbital speed of the satellite `= v_(0)=v = sqrt((GM)/(r ))`
and escape speed `v_(e )=sqrt(2)v`
`therefore` The K.E. of the object to escape from the satellite
`=(1)/(2)mv_(e )^(2)=(1)/(2)m. (sqrt(2)v)^(2)=(1)/(2)m(2v^(2))=mv^(2)`