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) $\dfrac{R}{3}$
Concept. Energy conservation with $v = \dfrac{v_e}{2}$, $v_e^2 = \dfrac{2GM}{R}$.
Step 1. Equation.
$$-\frac{GMm}{R} + \frac{GMm}{4R} = -\frac{GMm}{R + h} \;\Rightarrow\; R + h = \frac{4R}{3}$$
Step 2. Height. $h = \dfrac R3$.
Answer. $\dfrac R3$ (Option B).
Solution by Sreeraj P, M.Sc Physics