Two particles of mass m_{1} and m_{2} approac | vedclass

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(C) The gravitational force acting between the two masses $m_{1}$ and $m_{2}$ separated by a distance $r$ is given by Newton's law of gravitation:$F =

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acceleration of the particle of mass $m_{1}$ is proportional to $m_{2}$

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(C) The gravitational force acting between the two masses $m_{1}$ and $m_{2}$ separated by a distance $r$ is given by Newton's law of gravitation:$F = \frac{G m_{1} m_{2}}{r^{2}}$According to Newton's second law of motion, the force on mass $m_{1}$ is $F = m_{1} a_{1}$, where $a_{1}$ is the acceleration of mass $m_{1}$.Equating the two expressions:$m_{1} a_{1} = \frac{G m_{1} m_{2}}{r^{2}}$$a_{1} = \frac{G m_{2}}{r^{2}}$Since $G$ and $r$ are constant for the system at any given instant, we find that $a_{1} \propto m_{2}$.Similarly, for mass $m_{2}$, $a_{2} = \frac{G m_{1}}{r^{2}}$, which implies $a_{2} \propto m_{1}$.

Two particles of mass $m_{1}$ and $m_{2}$ approach each other due to their mutual gravitational attraction only. Then,

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