An object is allowed to fall freely from rest through a small vertical distance where…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

An object is allowed to fall freely from rest through a small vertical distance

h

where air resistance can be neglected. (i) Show that the time

t

taken to fall through the distance

h

is given by

t = \sqrt{\dfrac{2h}{g}}

. (ii) Using the value

g_{\text{Earth}} = 9.8\,\text{m/s}^2

and

g_{\text{Moon}} = \dfrac16 g_{\text{Earth}}

, calculate the ratio of times taken to fall

5\,\text{m}

on the Earth and on the Moon. (iii) Which time is larger? Give a brief reason, mentioning why atmospheric effects are neglected in this comparison.