Chapter 3, Problem 14TE

Two pumpkins are dropped from a high building through the air. One pumpkin is hollow and the other is filled with rocks. Which accelerates more? Defend your answer.

To determine

The comparison of the acceleration of the two pumpkins, one is filled with rocks and another is hollow.

Answer to Problem 14TE

Both pumpkins have equal acceleration because acceleration acting on a free-falling body is independent of its mass.

Explanation of Solution

Any object that is being acted upon only by the gravitational force is said to be in a state of free fall. In free fall, various other reaction forces acting on the body is considered as zero.

Write the expression for the gravitation force acting on a free-falling body.

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

Here,

$G$ is the gravitational constant

$M$ is the mass of a planet

$m$ is the mass of a body

$d$ is the separation distance

Write the expression for the force from Newton's second law.

$F=m\times a$

Here,

$a$ is the acceleration

On combining both expressions to get $a$.

$\begin{array}{ccc}m\times a& =& \frac{GMm}{d^2}\\ a& =& \frac{GM}{d^2}\end{array}$

This expression concludes that the acceleration acting on a free-falling body is independent of its mass. So, there is no meaning whether the pumpkin is hollow or filled with rocks both possess same acceleration.

Conclusion:

Therefore, both pumpkins have equal acceleration because acceleration acting on a free-falling body is independent of its mass.