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 ($g=10\text{ m/}{{\text{s}}^{\text{2}}}$):
A. $6\times {{10}^{3}}\text{ J}$
B. 6 J
C. 0.6 J
D. Zero
E. None of these.

Answer 1

The gravitational force on the bag is acting downwards while the girl is moving on a levelled road. The direction of force and displacement are hence perpendicular to each other. In other words, the angle ($\theta$) between force and displacement is $\text{90}{}^\circ$. We substitute this value of $\theta$ in the formula of work done as given below to calculate work.

Formula used:
Work done is given by,
$W=\overrightarrow{F}\cdot \overrightarrow{d}$
Where, F is force and d is displacement.
Therefore, work done can be written as:
$W=Fd\cos \theta$

Complete step by step solution:
Since angle between force and displacement is $\text{90}{}^\circ$, work done is calculated as:

& \text{ }W=Fd\cos \theta \\\ & \Rightarrow W=Fd\cos 90{}^\circ \\\ & \Rightarrow W=Fd\times 0 \\\ & \therefore W=0 \\\ \end{aligned}$$ Therefore, work done against the gravitational force is 0. The correct answer is option D. **Additional information:** When direction of force is parallel to displacement, the angle between them is $$\text{0}{}^\circ $$. In such cases, the work done is given by, $$\begin{aligned} & \text{ }W=Fd\cos \theta \\\ & \Rightarrow W=Fd\cos 0{}^\circ \\\ & \Rightarrow W=Fd\left( 1 \right) \\\ & \therefore W=Fd \\\ \end{aligned}$$ This gives us the maximum work done. When force and displacement is in the same direction, positive work is done and when force and displacement are in different directions, negative work is done. When the direction of force and displacement is perpendicular to each other, the work done is minimum, that is 0. **Note:** We should remember as a fact that when force and displacement are perpendicular to each other, the work done is zero. It is very important that we take the direction between force and displacement into consideration. If work done is calculated without considering this information, the answer will be incorrect.