Two particles of masses $1.0 k g$ and $2.0 k g$ are placed at a separation of $50 c m$ . 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

Given mass $m_{1} = 1 k g$ and $m_{2} = 2 k g$ , separation $d = 50 c m = 0.5 m$
The gravitational forces acting between them, $F = \frac{G m_{1} m_{2}}{d^{2}}$
Acceleration of particle of mass $m_{1}$ , $a_{m_{1}} = \frac{F}{m_{1}} = \frac{G m_{2}}{d^{2}} = \frac{6.67 \times 10^{- 11} \times 2}{{0.5}^{2}} = 5.336 \times 10^{- 10} m / s^{2}$

Acceleration of particle of mass $m_{2}$ , $a_{m_{2}} = \frac{F}{m_{2}} = \frac{G m_{1}}{d^{2}} = \frac{6.67 \times 10^{- 11} \times 1}{{0.5}^{2}} = 2.668 \times 10^{- 10} m / s^{2}$

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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.

Given mass m1=1kg and m2=2kg, separation d=50cm=0.5mThe gravitational forces acting between them, F=Gm1m2d2Acceleration of particle of mass m1, am1=Fm1=Gm2d2=6.67×10−11×20.52=5.336×10−10m/s2Acceleration of particle of mass m2, am2=Fm2=Gm1d2=6.67×10−11×10.52=2.668×10−10m/s2

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