Question

Four particles each of mass $\text{M}$, are located at the vertices of a square with side $\text{L}$. The gravitational potential due to this at the center of the square is:-

• A. $-\sqrt{32}\frac{GM}{L}$
• B. $\sqrt{64}\frac{GM}{L^2}$
• C. Zero
• D. $-\sqrt{32}\frac{GM}{L}$

Answer 1

The correct option is A $-\sqrt{32}\frac{GM}{L}$


As we know that the gravitational potential is given by:-
$V=–\frac{GM}{R}$

Potential at the center due to a single mass,

$\frac{-GM}{=\frac{L}{\sqrt{2}}}$

Potential at the center due to all four masses,

$=-4\frac{GM}{\frac{L}{\sqrt{2}}}=-4\sqrt{2}\frac{GM}{L}=-\sqrt{32}\frac{GM}{L}$

Why this question? The question involves the calculation of gravitational potential at a random point.