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Gravitational Force

Two particles...

Question

Two particles of masses 1kg and 2kg are placed at a separation of 50 cm. Assuming that the only forces acting on the particles are their mutual gravitation. The initial accelerations of the two particles are

6 \times 10^{- 10} m s^{- 2}

and

8.7 \times 10^{- 10} m / s^{2}

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5.3 \times 10^{- 10} m s^{- 2}

and

2.65 \times 10^{- 10} m / s^{2}

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1.57 \times 10^{- 10} m s^{- 2}

and

43.4 \times 10^{- 10} m / s^{2}

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1.67 \times 10^{- 10} m s^{- 2}

and

1.08 \times 10^{- 10} m / s^{2}

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Solution

The correct option is B $5.3 \times 10^{- 10} m s^{- 2}$ and $2.65 \times 10^{- 10} m / s^{2}$
Acceleration is $\frac{G m_{1} m_{2}}{r^{2}}$
$50 c m = 0.5 m$
$r^{2} = {0.5}^{2}$
$= 0.25$
$G = 6. 67 \times 10^{- 11}$
$M_{1} M_{2} = 2 \times 1 = 2$
Force $= 6.67 \times 2 \times 10^{- 11} / 0.25$
$5.336 \times 10^{- 10}$ Newton
Acceleration of particles are F/M SECOND LAW OF MOTION
A of particle one is $(5.336 \times 10^{- 10}) / 1$
$= 5.33 \times 10^{- 10} m / s^{2}$
A of particle 2 is $(5.336 \times 10^{- 10}) / 2$
$= 2.668 \times 10^{- 10} m / s^{2}$

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