99 Percentile Qs Bank for JEE MainPhysicsGravitation
A particle is projected with velocity k v e in the vertically upward direction from the ground into space ( v e is escape velocity and k < 1 ). The maximum height from the centre of the earth to which it can reach is
Options
- AR k 2 + 1
- Bk 2 R 1 - k 2
- CR 1 - k 2
- Dk 2 R k 2 + 1
Correct answer
C. R 1 - k 2
Step-by-step solution
Total energy of surface = Total energy at h height ⇒ 1 2 m k v e 2 + - G M m R = 0 + - G M m R + h ⇒ k 2 1 2 m v e 2 + - G M m R = - G M m R + h ⇒ k 2 1 2 m 2 G M R - G M m R = - G M m R + h ⇒ 1 R - k 2 R = 1 R + h ⇒ 1 - k 2 R = 1 R + h ⇒ R + h = R 1 - k 2