Question

Consider the following statements:
A. The acceleration due to gravity on the Moon is equal to that of the Earth.
B. The value of G is independent of the nature, size and mass of the interacting bodies.
Which of these statement(s) is/are correct?

• A. A only
• B. B only
• C. Both A and B
• D. Neither A nor B

Answer 1

The correct option is B B only

The acceleration due to gravity on the surface of a planet is given by:
$g=\frac{GM}{R^2}$
where:
$G=6.67\times {10}^{-11}:\text{Gravitational constant}$
M: Mass of the planet
R: Radius of the planet

Mass of Moon is, $M_m\approx 7.34\times {10}^{22}kg$
Radius of Moon is, $R_m\approx 1.73\times {10}^{6}m$

Plugging in the above values, we get the acceleration due to gravity on the Moon is:
$g_m=1.62m{s}^{-2}$

This is approximately 1/6${}^{th}$ that of the acceleration due to gravity ($9.8m{s}^{-2}$) on the Earth.

The value of G is independent of the nature, size and mass of the interacting bodies. It is the universal gravitational constant.