Question

The earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of Earth. The escape velocity of a body from this platform is $kv$, where $v$ is its escape velocity from the surface of the earth. The value of $k$ is

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\sqrt{2}$

Answer 1

Answer: (A)

$\frac{1}{\sqrt{2}}$

Here, $v=\sqrt{\frac{2GM}{R}}$ and $kv=\sqrt{\frac{2GM}{R+R}}$
Solving $k=\frac{1}{\sqrt{2}}$