Two particles of masses $1.0$ kg and $2.0$ kg are placed at a separation of $50$ cm. Assuming that the only forces acting on the particles are their mutual gravitation, find the initial accelerations of the two particles.

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Solution

The force between the particles will be

$F = \frac{G m_{1} m_{2}}{d^{2}}$

Also, $a_{1} = \frac{F}{m_{1}} = \frac{G m_{2}}{d^{2}} = \frac{(6.67 X 10^{- 11}) (2)}{{0.5}^{2}} = 5.34 X 10^{- 10} m / s^{2}$

$a_{2} = \frac{F}{m_{2}} = \frac{G m_{1}}{d^{2}} = \frac{(6.67 X 10^{- 11}) (1)}{{0.5}^{2}} = 2.67 X 10^{- 10} m / s^{2}$

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Two particles of masses 1.0kg and 2.0kg are placed at a separation of 50cm. Assuming that the only forces acting on the particles are their mutual gravitation, find the initial accelerations of the two particles.

The force between the particles will beF=Gm1m2d2Also, a1=Fm1=Gm2d2=(6.67X10−11)(2)0.52=5.34X10−10m/s2a2=Fm2=Gm1d2=(6.67X10−11)(1)0.52=2.67X10−10m/s2

Two particles of masses $1.0$ kg and $2.0$ kg are placed at a separation of $50$ cm. Assuming that the only forces acting on the particles are their mutual gravitation, find the initial accelerations of the two particles.