SATHEE: Gravitation Question 324

Gravitation Question 324

Question: Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Then, velocity of a particle is given by

Options:

A) $[{[\frac{G m}{r} (\frac{1 + 2 \sqrt{2}}{4})]}^{\frac{1}{2}}]$

B) $[\sqrt{\frac{G m}{r}}]$

C) $[\sqrt{\frac{G m}{r}} (1 + 2 \sqrt{2})]$

D) $[a {[\frac{1}{2} \frac{G m}{r} (\frac{1 + 2 \sqrt{2}}{2})]}^{\frac{1}{2}}]$

Show Answer

Answer:

Correct Answer: A

Solution:

Centripetal force = net gravitational force

$[\Rightarrow \frac{m v_{0}^{2}}{r} = 2 F \cos 45^{o} + F_{1} = \frac{2 G m^{2}}{{(\sqrt{2})}^{2}} \frac{1}{\sqrt{2}} + \frac{G m}{4 r^{2}}]$

$[\frac{m v_{0}^{2}}{r} = \frac{G m}{4 r^{2}} [2 \sqrt{2} + 1]]$ $[\Rightarrow v_{0} = {[\frac{G m (2 \sqrt{2} + 1)}{4 r}]}^{\frac{1}{2}}]$

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Gravitation Question 324

Question: Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Then, velocity of a particle is given by

Options:

Answer:

Solution:

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