Question

The distance travelled by a freely falling body is proportional to

• A. the mass of the body
• B. the square of the acceleration due to gravity
• C. the square of the time of fall
• D. the time of fall

Answer 1

The correct option is C

the square of the time of fall

Explanation of the correct option:

(C) the square of the time of fall

Using the 2nd equation of motion

:$$\begin{gathered} \mathrm{s}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2 \\ \mathrm{where}\mathrm{a}=\mathrm{acceleration}\mathrm{due}\mathrm{to}\mathrm{gravity} \\ \mathrm{t}=\mathrm{time}\mathrm{taken}\mathrm{to}\mathrm{fall}\mathrm{to}\mathrm{the}\mathrm{ground} \\ \mathrm{s}=\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{a}\mathrm{freely}\mathrm{falling}\mathrm{body} \\ \mathrm{u}=\mathrm{initial}\mathrm{velocity}\mathrm{of}\mathrm{the}\mathrm{body},\mathrm{as}\mathrm{the}\mathrm{body}\mathrm{is}\mathrm{in}\mathrm{a}\mathrm{free}\mathrm{fall},\mathrm{it}\mathrm{means}\mathrm{that}\mathrm{the}\mathrm{inital}\mathrm{velocity}\mathrm{of}\mathrm{the}\mathrm{body}\mathrm{will}\mathrm{be}0. \\ \mathrm{s}=\frac{1}{2}{\mathrm{at}}^2 \\ \mathrm{s}\propto {\mathrm{t}}^2 \end{gathered}$$

Thus, the distance travelled by a freely falling body is proportional to the square of the time of fall.

Explanation of the incorrect options:

(A) the mass of the body

Distance travelled by a body is not related to the mass of a body in a free fall.

(B) the square of the acceleration due to gravity

In a free fall, the distance travelled by any object depends on the acceleration due to gravity which is the same for every object and is equal to 9.8 m/s².

(D) the time of fall

Distance travelled by a body in a free fall depends on the time of fall but it is not directly proportional to it.

Hence, option C is correct.