Question

Suppose a planet exists, whose mass and radius both are half of the earth. Calculate the acceleration due to gravity on the surface of this planet.
The universal law of gravitation states that every object exerts a gravitational force of attraction on every other object. If this is true, then why don't we see the various objects in a room moving towards one another?

Answer 1

Acceleration due to gravity

g = $\frac{GM}{R^2}$

Here, M is the mass of the planet and R is the radius on earth, g = 9.8 $\frac{m}{s^2}$

On the pllanet g' = $\frac{GM}{R^2}$ = $\frac{GM}{2(\frac{R}{2}{)}^2}$ = 2 g

Thus, acceleration due to gravity on the planet is

g' = 2g = $2\times 9.8$ = 19.6 $\frac{m}{s^2}$

The magnitude of the gravitational force acting on either of two 1 kg masses separated by 1 meter as a result of one another is just $6.67\times {10}^{-11}$ N.

Whereas, the frictional force acting on either mass (assuming them to be made of rubber and resting on concrete) is approximately 10 N.

So the force that restrains their movement (friction) is approximately 150 billion times stronger than the force that could move them (gravity).