A body is projected vertically upwards from the surface of the earth. If its kinetic energy is equal to half of its minimum value required to escape from the gravitational influece, then the height upto which it rises is

Options

A. 4R
B. 3R
C. 2R
D. R

Answer

D

Explanation

Given K.E. `=(1)/(2)` (K.E.) escape
`=(1)/(2)((1)/(2)mv_(e)^(2))=(1)/(4)xx m((2GM)/(R ))=(GMm)/(2R)`
For upward motion, loss in K.E. = gain in P.E.
`therefore (GMm)/(2R)=-((GMm)/(R+h))-(-(GMm)/(R ))`
`therefore (1)/(2R)=(1)//(R )-(1)/(R+h)`
`therefore (1)/(R+h)=(1)/(2R)" " therefore h = R`