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

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

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