Q 11-07-016NEETJEE MainEAMCET 2009 (Engineering)Top questionMedium
A body is projected vertically upwards from the surface of the earth with a velocity equal to half of the escape velocity of the earth. If $R$ is the radius of the earth, the maximum height attained by the body from the surface of the earth is
Answer: (B) $\dfrac{R}{3}$
With $v_e^2 = \dfrac{2GM}{R}$ and $v = \dfrac{v_e}{2}$:
$$-\frac{GMm}{R} + \frac{1}{2}m\cdot\frac{GM}{2R} = -\frac{GMm}{R + h} \;\Rightarrow\; \frac{3}{4R} = \frac{1}{R + h}$$
$$R + h = \frac{4R}{3} \;\Rightarrow\; h = \frac{R}{3}$$
Solution by Sreeraj P, M.Sc Physics