Question

A girl is carrying a school bag of 3 kg mass on her back and moves 200 m on a levelled road. The work done against the gravitational force will be ($g = 10\,m{s^{ - 2}}$).
A. $6 \times {10^3}\,J$
B. 6 J
C. 0.6 J
D. Zero

Answer 1

Find out the angle made by the gravitational force with the displacement vector of the school bag. Use the formula for the work done by the net force.

Formula used:
$W = Fd\cos \theta$
Here, F is the net force, d is the displacement of the body and $\theta$ is the angle between force F and displacement vector d.

Complete step by step answer:
We know that, if the net force makes angle $\theta$ with the displacement vector of the body, the work done by the net force is given as,
$W = Fd\cos \theta$
Here, F is the net force, d is the displacement of the body and $\theta$ is the angle between force F and displacement vector d.
In this case, the net force is the gravitational force acting on the school bag. The direction of the gravitational force is always in the downward direction.
Now, we can use the above formula to determine the work done by the gravitational force.
$W = {F_g}d\cos \theta$
Since the angle between gravitational force and displacement of the body is $90^\circ$. The above equation becomes,
$W = {F_g}d\cos \left( {90^\circ } \right)$
$\Rightarrow W = {F_g}d\left( 0 \right)$
$\Rightarrow W = 0\,J$
Therefore, the work done by the gravitational force on the school bag is zero.

So, the correct answer is “Option D”.

Note:
While solving such types of questions, students should note that the gravitational force does work on the body that has at least slight displacement in the vertical direction.
We can use the above formula to determine the work done by the gravitational force.