Question

Four equal masses (each of mass $M$) are placed at the corners of a square of side $a$. The escape velocity of a body from the centre $O$ of the square is

• A. $\sqrt[4]{4\frac{2GM}{a}}$
• B. $\sqrt{\frac{8\sqrt{2}GM}{a}}$
• C. $\frac{4GM}{a}$
• D. $\sqrt{\frac{4\sqrt{2}GM}{a}}$

Answer 1

The correct option is B $\sqrt{\frac{8\sqrt{2}GM}{a}}$

Potential energy of particle at the centre of square
$=-4\left(\frac{GMm}{\frac{a}{\sqrt{2}}}\right)$
$\therefore -4\left(\frac{GMm}{a/\sqrt{2}}\right)+\frac{1}{2}m{v}^2=0\Rightarrow v^2=\frac{8\sqrt{2}GM}{a}$