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  • 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.Velocity of a particle is given

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.Velocity of a particle is given by

 

                                               

Option: 1

\left [ \frac{Gm}{r} \left ( \frac{1+2\sqrt{2}}{4} \right )\right ]^{\frac{1}{2}}

 

 

 


Option: 2

\sqrt[3]{\frac{Gm}{r}}


Option: 3

\sqrt{\frac{Gm}{r}\left ( 1+2\sqrt{2} \right )}


Option: 4

\left [ \frac{1}{2} \frac{Gm}{r}\left ( \frac{1+\sqrt{2}}{2} \right )\right ]^\frac{1}{2}


Answers (1)

best_answer

 

According to Newton's Law of Gravitation -

 F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}

 For the above figure Applying Centripetal force = net gravitational force

\frac{mv^{2}_{0}}{r}=2F\cos 45^{0}+F_1= \frac{2Gm^{2}}{\left ( \sqrt{2r} \right )^{2}}\frac{1}{\sqrt{2}}+\frac{Gm^{2}}{4r^{2}} 

\frac{mv^{2}_{0}}{r}=\frac{Gm^{2}}{4r^{2}}\left [ 2\sqrt{2}+1 \right ]\Rightarrow v_0=\left ( \frac{Gm\left ( 2\sqrt{2}+1 \right )}{4r} \right )^{\frac{1}{2}}

 

 

Posted by

manish painkra

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