Question

A coolie X is carrying a load on his head climbs up a slope and another Y carrying the identical load on his head moves the same distance on the frictionless horizontal platform. Who does more work?
A. X
B. Y
C. Both A and B.
D. Cannot say

Answer 1

Hint: The amount of work done strongly depends on the angle between the force and displacement.

Complete step by step answer:
Refer to the figure below for an object moving up the inclined plane:

Ability to do work is called energy and the energy dissipated is equal to work done.
Express the relation for work done:
$W=Fs\cos \theta$

Here $W$ is the work done, $F$ is the force acting on the body, $s$ is the displacement and $\theta$ is the angle between the force and the displacement.
In case of Y when it is moving on a flat surface the angle between force and displacement is ${90}^{\circ }$, and $N$ is equal to normal reaction.

Therefore, the work done in case of Y becomes,
$$\begin{gathered} W=F\times s\times \cos {90}^{\circ } \\ W=mg\times s\times \cos {90}^{\circ } \\ W=0 \end{gathered}$$
Here, $m$ is the mass of the body and $g$ is the acceleration due to gravity.
Whereas, in case of X, the force and displacement are not perpendicular. Therefore,
$W\ne 0$

Therefore, X does more work as compared to Y.

Hence the correct option is (A).

Note: Work done by X while moving up the slope is, $W=(F-mg\sin \theta )\times s$. When X is moving up the slope, it has to encounter friction down the slope and has to work against gravity. But Y is moving on a frictionless surface.