Question

Two particles each of mass $1Kg$ are placed at $p$ and $Q$ such that $PQ=OQ=L$. The gravitational force experienced by another $1Kg$ mass placed at $R$, where $OR=L$ is

• A. $\frac{G}{\sqrt{2}{L}^2}$ along $RO$
• B. $\frac{G}{\sqrt{2}{L}^2}$ along $OP$
• C. $\frac{G}{L^2}$ along $PQ$
• D. $Zero$

Answer 1

The correct option is A $\frac{G}{\sqrt{2}{L}^2}$ along $RO$

$F_{PR}=\frac{GMm}{(\sqrt{2}L{)}^2}=[cos{45}^0\hat{i}+sin{45}^0\hat{j}]$

$F_{QR}=\frac{GMm}{(\sqrt{2}L{)}^2}=[cos{45}^0\hat{i}+sin{45}^0\hat{j}]$

Therefore,

$F_{net}=F_{PR}+F_{QR}$

$=\frac{GMm}{2L^2}[cos{45}^0\hat{i}+sin{45}^0\hat{j}-cos{45}^0\hat{i}+sin{45}^0\hat{j}]$

$=\frac{GMm}{2L^2}\left[2sin{45}^0\hat{j}\right]$

$=\frac{GMm}{2L^2}\times 2\times \frac{1}{\sqrt{2}}\hat{j}$

$=\frac{GMm}{\sqrt{2}{L}^2}\hat{j}$

Given,

Mass, $=1kg$

Then,

$F_{net}=\frac{G}{\sqrt{2}{L}^2}\hat{j}$ (along $RO$)