99 Percentile Qs Bank for JEE MainPhysicsGravitation
A body is thrown from the surface of the earth with velocity 'V' m s . The maximum height above the earth's surface upto which it will reach is ( R = radius of earth, g = acceleration due to gravity)
Options
- AVR ² g R - V
- BV ² R 2 gR - V ²
- C2 R V²(R-1)
- DVR 2 R-V
Correct answer
B. V ² R 2 gR - V ²
Step-by-step solution
aligned 1 2 mu ² &=- GMm R + h - (- GMm R )= GMm R - GMm R + h &= GMm [ 1 R - 1 R + h ] u ² &=2 GM [ 1 R - 1 R + h ] u ² &=2 gR ² [ R + h - R R ( R + h ) ] u ² &=2 gR [ h R + h ] u ² 2 gR &= [ h R + h ] R + h R = 2 gR u ² R h +1 &= 2 gR u ² R h &= 2 gR u ² -1= 2 gR - u ² u ² h = Ru ² 2 gR - u ² aligned