Question 91: Gravitation

Question

Four identical particles of mass $$m$$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $$\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{L^2}$$, the length of the sides of the square is

Accepted Answer

$$\begin{aligned}
& F_{	ext {net }}=\sqrt{2} F+F^{\prime} \
& F=\frac{G m^2}{a^2} 	ext { and } F^{\prime}=\frac{G^2}{(\sqrt{2} \mathrm{a})^2} \
& F_{	ext {net }}=\sqrt{2} \frac{\mathrm{Gm}^2}{\mathrm{a}^2}+\frac{\mathrm{Gm}^2}{2 \mathrm{a}^2} \
& \left(\frac{2 \sqrt{2}+1}{32}ight) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}=\frac{\mathrm{Gm}^2}{\mathrm{a}^2}\left(\frac{2 \sqrt{2}+1}{2}ight) \
& \mathrm{a}=4 \mathrm{~L}
\end{aligned}$$

Answer

4L

Answer

3L

Answer

2L

Answer

$$\frac{L}{2}$$

Gravitation

Four identical particles of mass $m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{L^2}$, the length of the sides of the square is

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