Question

a) The G Force between two objects is F. How will this force change when the distance
between them is reduced to half?
b) Would the rate of fall of a sheet paper and one that is crumpled into a ball be different in:
i) Air.
ii) Vacuum.
Justify your answer for each case.​

Answer 1

Answer:

a) Gravitational force = F

The formula for the force of gravity is

F = $\frac{GMm}{d^2}$

If the distance is halved,

F = $\frac{GMm}{(d/2)^2}$

∴ F = $\frac{GMm}{d/4}$

F =   4 *  $\frac{GMm}{d^2}$

∴ The force will be quadrupled (increased 4 times) when the distance is halved.

b) The rate of fall of a sheet of paper and a crumpled ball in air would be different due to the different amount of air resistance acting on them because of the different amount of surface areas exposed to the air resistance (the ball is an aerodynamic object whereas a flat sheet of paper is not). Whereas, in vacuum, there will be no difference in the rate of fall between the two mentioned bodies as there is only one force acting on the bodies, i.e., gravitational force. As there is no air friction, the bodies will fall at the same rate in vacuum.