Question

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

• A. 44563
• B. $\sqrt 2 $
• C. $ \frac{1}{\sqrt 2} $
• D. 44564

Answer 1

The Correct Option is C

According to question and by using COME $-\frac{ GMm }{ R + R }+\frac{1}{2} m ( fv )^{2}=0+0$ $\Rightarrow fv =\sqrt{\frac{ GM }{ R }}$ but $ v =\sqrt{\frac{2 GM }{ R }}$ Therefore $f \sqrt{\frac{2 GM }{ R }}=\sqrt{\frac{ GM }{ R }}$ $ \Rightarrow f =\frac{1}{\sqrt{2}}$