Question

The acceleration of moon with respect to earth is 0.0027 m $s^{-3}$ and the acceleration of an apple falling on earth's surface is about 10 m $s^{-2}$. Assume that the radius of the moon is one-fourth of the earth's radius. If the moon is stopped for an instant and then released, it will fall towards the earth.

The acceleration of the moon just before it strikes the earth is

• A. $10m/s^2$
• B. $0.0027m/s^2$
• C. $6.4m/s^2$
• D. $5.0m/s^2$

Answer 1

Answer: (C)

$6.4m/s^2$

When the moon strikes the earth its center is $R/4$ above the surface of the earth. So the acceleration of the moon will be calculated at $R+R/4=5R/4$ away from the center of the earth.

Since the acceleration is inversely proportional to the square of the distance,

The acceleration of the moon at the time of strike = $g\times {\frac{R}{\frac{5R}{4}}}^2=g\times {\frac{4}{5}}^2=\frac{16g}{25}=\frac{160}{25}=6.4m/s².$