Question

A body is projected up with $\frac{3}{4}$ the escape velocity from earths surface. The height reached by the body is

• A. $\frac{7}{9}R$
• B. $\frac{9}{7}R$
• C. $\frac{7}{3}R$
• D. $\frac{3}{7}R$

Answer 1

The correct option is B $\frac{9}{7}R$

Let the height reached by the body be h. Its distance from the centre of earth at maximum height will be R+h.

Hence, conserving energy and using $V_e=\sqrt{\frac{2GM}{R}}$,

$\frac{1}{2}m\left(\frac{9}{16}\right)V_e^2-\frac{GMm}{R}=-\frac{GMm}{R+h}$

$-\frac{7}{16}\frac{GMm}{R}=-\frac{GMm}{R+h}$

$R+h=\frac{16}{7}R$

$h=\frac{9}{7}R$