Question

A body is projected up with a velocity equal to $\sqrt{\frac{9 G M}{8 R}}$ , where $M$ is the mass of the earth and $R$ is the radius of the earth. The maximum distance it reaches from the centre of the earth is

• A. $\frac{10 R}{9}$
• B. $\frac{16 R}{7}$
• C. $\frac{10 R}{3}$
• D. $\frac{9 R}{8}$

Answer 1

Answer: (B)

Let us assume that the maximum distance of the body from the centre of the earth is $h$ .
Applying the conservation of mechanical energy, we get
$\frac{1}{2}m\left(\sqrt{\frac{9 G M}{8 R}}\right)^{2}-\frac{G M m}{R}=-\frac{G M m}{h}$
$-\frac{7}{16}\frac{G M m}{R}=-\frac{G M m}{h}$
$\Rightarrow h=\frac{16 R}{7}$