There is crater of depth `R//100` on the surface of the moon (raduis `R`). A projectile is fired vertically upwards from the crater with a velocity, which is equal to the escape velocity `v` from the surface of the moon. The maximum height attained by the projectile, is :

Options

A. `90R`
B. `95R`
C. `99.5R`
D. `50R`

Answer

C

Explanation

Speed of particle at `A`, `v_(A)`=escape velocity on the surface of earth `sqrt((2GM)/R)` at highest point `B,v_(B)=0`
Applying conservation of mechanical energy decrease in kinetic energy =increases in gravitational potential energy
`=1/2mv_(A)^(2)=U_(B)-U_(A)=m(V_(B)-V_(A))`
`(V_(A)^(2))/2=V_(B)-V_(A)`
`(GM)/R=-(GM)/(R+h)-[(-GM)/(R^(3))[(1.5R^(2))-0.5(R-R/100)^(2)]]`
`1/R=-1(R+h)+3/(2R)-(1/2)(99/100)^(2).1/R`
Solving this equations, we get `h=99.5 R`