Two bodies of equal masses revolve in circula | vedclass

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(B) The formula for centripetal force $F$ is given by $F = m\omega^2 R$,where $m$ is the mass,$\omega$ is the angular velocity,and $R$ is the radius o

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$\frac{R_1}{R_2}$

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(B) The formula for centripetal force $F$ is given by $F = m\omega^2 R$,where $m$ is the mass,$\omega$ is the angular velocity,and $R$ is the radius of the orbit.Since the angular velocity $\omega = \frac{2\pi}{T}$,where $T$ is the time period,we can write the force as $F = m(\frac{2\pi}{T})^2 R = m \frac{4\pi^2}{T^2} R$.Given that the masses $m$ and the time periods $T$ are the same for both bodies,the expression $\frac{m 4\pi^2}{T^2}$ is constant.Therefore,the centripetal force is directly proportional to the radius,$F \propto R$.Thus,the ratio of the centripetal forces is $\frac{F_1}{F_2} = \frac{R_1}{R_2}$.

Two bodies of equal masses revolve in circular orbits of radii $R_1$ and $R_2$ with the same period. Their centripetal forces are in the ratio:

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