Chapter 3, Problem 6RAT

A heavy rock and a light rock in free fall have the same acceleration. The reason the heavy rock does not have more acceleration is

(a) the force of gravity on each is the same.

(b) there is no air resistance.

(c) the inertia of both rocks is the same.

(d) All of these.

(e) None of these

To determine

The correct option for the statement " A heavy rock and a light rock in free fall have the same acceleration. Thereason the heavy rock does not have more acceleration is".

Answer to Problem 6RAT

The correct option for the statement " A heavy rock and a light rock in free fall have the same acceleration. The reason the heavy rock does not have more acceleration is" is option (d).

Explanation of Solution

When the body is under free-falling, only the gravitational force is act on it, where other forces are neglected, such as air resistance or drag. Any object that is being acted upon only by the gravitational force is said to be in a state of free fall.

Write the expression for 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 on a body by Newton's second law.

$F=m\times a$

Here,

m is the mass of a body

a is the acceleration of a body

By combining both expressions.

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

This expression concludes that the acceleration acting on a free-falling body is independent of its mass, so that is the reason behind both heavy and light rock having the same acceleration.

Conclusion:

Therefore, the correct option for the statement " A heavy rock and a light rock in free fall have the same acceleration. The reason the heavy rock does not have more acceleration is" is option (d).