Question

According to the chart, on which planet would a ball fall the fastest?

Planet	Earth	Jupiter	Neptune	Saturn
Acceleration due to gravity	10	26	14	12

A. Jupiter
B. Saturn
C. Neptune
D. Earth

Answer 1

Hint: Fastest here means, highest velocity. Use the kinematic equation of motion $v^2 – u^2 =2as$ to determine an analogous equation of motion for a falling body. You will arrive at a relation between the velocity and acceleration due to gravity from which you can deduce on which planet the ball falls with a greater velocity.

Formula Used:
Equation for velocity of a falling body: $v=\sqrt{2gh}$

Complete step-by-step answer:
We are supposed to determine on which planet the ball would fall the “fastest”, which means that we need to determine on which planet the ball falls with a relatively greater velocity.
We can derive a relation between velocity and acceleration due to gravity from the kinematic equation of motion $v^2 -u^2 = 2aS$, where v is the final velocity reached before coming to a stop, u is the initial velocity, a is the acceleration, and S is the distance travelled.
Now, in our scenario, we have $u = 0$, $S=h$ since the body is just dropped from a height h, and $a =g$ where g is the acceleration due to gravity.
Therefore, we obtain an equation for our falling body: $v^2 = 2gh \Rightarrow v = \sqrt{2gh}$.
Assuming that the ball is dropped from the same height on every planet, we have
 $v \propto \sqrt{g}$
This means that the velocity with which a body falls will be maximum for that planet which has the highest acceleration due to gravity.
From the table, we see that Jupiter has the highest acceleration due to gravity, which means that the ball would fall the fastest on Jupiter.
Thus, the correct choice would be: A. Jupiter.

Note: The value of g is different for different planets because of their different sizes, masses and densities, which is conclusive from the table given to us. However, remember that the value of g remains the same for all bodies on the surface of the earth and the value of g varies with the height and depth from the surface of the earth.