Question

Four particles of masses $m,2m,3m$ and $4m$ are placed at the corners of a square of side length $a$. The gravitational force on a particle on a particle of mass $m$ placed at the centre of the square is

• A. $4\sqrt{2}\frac{G{m}^2}{a^2}$
• B. $\frac{3\sqrt{2}G{m}^2}{a^2}$
• C. $\frac{2\sqrt{2}G{m}^2}{a^2}$
• D. $\frac{\sqrt{2}G{m}^2}{a^2}$

Answer 1

The correct option is A $4\sqrt{2}\frac{G{m}^2}{a^2}$

Side of square=a

r=$\frac{1}{2}\times Diagonallength=\frac{1}{2}\sqrt{2}\times a=\frac{a}{\sqrt{2}}$

Along a diagonal gravitational force=$\frac{2G{m}^2}{(\frac{a}{\sqrt{2}}{)}^2}=\frac{4G{m}^2}{a^2}$

Along the second diagonal gravitational force=$\frac{2G{m}^2}{(\frac{a}{\sqrt{2}}{)}^2}=\frac{4G{m}^2}{a^2}$

Resultant=$\frac{4\sqrt{2}G{m}^2}{a^2}$