Question

A man starts walking from a point on the surface of the earth (assumed smooth) and reaches the diagonally opposite point. What is the work done by him?
A. Zero
B. Positive
C. Negative
D. None of the above

Answer 1

Hint:Before we start proceeding with this problem let us understand the term displacement and work done. When a force is applied, the object changes its position which is known as displacement. Since it is a vector quantity it has both direction and magnitude. Work is nothing but a force needed to move an object from one place to another.

Formula Used:
The formula to find the work done is,
\[W = \overrightarrow F \cdot \overrightarrow S \]
Where, \[\overrightarrow F \] is force applied and \[\overrightarrow S \] is displacement.

Complete step by step solution:
Consider a man who starts walking on the surface of the earth from one point and reaches another opposite point diagonally. Now we need to find the work done by the man in moving from one point to another. As they said that the surface is smooth so the work done against friction is zero.

When a man starts walking on the surface of the earth from one point and reaches another opposite point diagonally then, the displacement and force of gravity are perpendicular to each other, so the work done against gravity is zero. This can be explained as,
\[W = \overrightarrow F \cdot \overrightarrow S \]
\[\Rightarrow W = F \cdot S\cos \theta \]
When the angle between the force of gravity and the displacement is \[{90^0}\], because the force of gravity and the displacement are perpendicular to each other. Then,
\[W = F \cdot S\cos {90^0}\]
\[\therefore W = 0\]
Therefore, the work done by the man is zero.

Hence, option A is the correct answer.

Note: We can say that the work done is zero because the Work done on an object depends on the amount of force F causing the work, the displacement d that is experienced by the object. So, if no displacement occurs then the work done upon the object is zero.