Question

1. Does the acceleration due to gravity depend on the mass of a body?
2. To estimate the height of a bridge over a river, a stone is dropped freely in the river from the bridge. The stone takes 2 seconds to touch the water surface in the river. Calculate the height of the bridge from the water level $(g=9.8m{s}^{-2})$
[3 MARKS]

Answer 1

Correct answer: 1 Mark
Problem: 2 Marks

1. From Universal law of gravitation we have, $F=\frac{GMm}{r^2}$ ......(1)
where F is the gravitational force between the earth and the object, M is mass of the earth, m is mass of the object, r is the distance between them, and G is the universal gravitational constant.
We know for an object of mass m,
$F=mg$ ......(2)
where $g$ is the acceleration due to gravity.
On comparing (1) and (2), we can write,
$mg=\frac{GMm}{r^2}$
$\Rightarrow g=\frac{GM}{r^2}$
Therefore, acceleration due to gravity does not depend on mass of the object.

2. Given, time taken, $t=2s$, acceleration due to gravity, $g=9.8m{s}^{-2}$ and initial velocity, $u=0$ (initially the stone is at rest)
Let height of the bridge be $s$
From second equation of motion,
$s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow s=0\times 2+\frac{1}{2}\times 9.8\times 2^2$
$\Rightarrow s=19.6m$

Thus, the height of bridge above the water level is 19.6 metres.