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Question: A body is projected vertically upwards from the surface of a planet of radius R with a velocity equa...

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

A

R/3

B

R/2

C

R/4

D

R/5

Answer

R/3

Explanation

Solution

If body is projected with velocity v (v<ve)\left( v < v _ { e } \right)then height up to which it will rise, h=Rve2v2−1h = \frac { R } { \frac { v _ { e } ^ { 2 } } { v ^ { 2 } } - 1 }

v=ve2v = \frac { v _ { e } } { 2 } (given) ∴ h=R(veve/2)2−1=R4−1=R3h = \frac { R } { \left( \frac { v _ { e } } { v _ { e } / 2 } \right) ^ { 2 } - 1 } = \frac { R } { 4 - 1 } = \frac { R } { 3 }