First slide

Gravitational force and laws

Question

If three uniform spheres, each having mass M and radius R, are kept in such away that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

Moderate

A

$\frac{{GM}^{2}}{4 r^{2}}$
B

$\frac{2 {GM}^{2}}{r^{2}}$
C

$\frac{2 {GM}^{2}}{4 r^{2}}$
D

$\frac{\sqrt{3} {GM}^{2}}{4 r^{2}}$

Solution

$\begin{array}{l} \vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2} \\ As |{\vec{F}}_{1}| = |{\vec{F}}_{2}| \\ ∴ | \vec{F} | = 2 F_{1} \cos 30^{\circ} \\ = 2 \frac{{GM}^{2}}{(2 r)^{2}} \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{4} \frac{{GM}^{2}}{r^{2}} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App