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

Options

A. `10R//9`
B. `16R//7`
C. `9R//8`
D. `10R//3`

Answer

B

Explanation

`v=(3)/(4)v_(e)`
`K.E. =(1)/(2) mv^(2)=(1)/(2)m ((3)/(4)v_(e))^(2)=(9)/(32) mv_(e)^(2)`
`=(9)/(32)m ((2GM)/(R))`
`(9)/(16) (GMm)/(R)-(GMm)/(R)=-(GMm)/(r)`
`r=(16R)/(7)`