A body is projected up with a velocity up with a velocity equal to `3/4` of the escape velocity from the surface of the earth . The height it reaches is ( Radius of the earth = R )

Options

A. `10R/9`
B. `9R/7`
C. `9R/8`
D. `10R/3`

Answer

B

Explanation

Maximum height attained by the body is given by ,
h= `( v^2 R)/ (2gR-v^2)`
where
`v= 3/4.v_e`
v= `(3/4)sqrt 2gR`
h= `((9)/(16)((2gR)R)/(2gR)- (9/16)2gR)`= `((9/16))(2gR^2)2gR-(1-(9)/16)`
Therefore h= `(9/16)(R)/(7/16)= (9R)/(7)`