Question

An ant drags a piece of a sweet from origin $(0,0)$ to $(3,4)$ in the co-ordinate axes. What is the work done by the ant if it applies a force of $1N$ and takes the shortest path?
$(1\text{unit}=1\text{metre}$)

• A. 1 J
• B. 3 J
• C. 5 J
• D. 7 J

Answer 1

The correct option is C

5 J

Displacement of the sweet from $(0,0)$ to $(3,4)$ is equal to its final distance from the origin.
Displacement:
$s=\sqrt{3^2+4^2}=\sqrt{9+16}=5m$

Force applied by the ant is along displacement as it is dragging the sweet by itself. It is given as:
$F=1N$

By definition, work done by a force is the product of force and displacement along the force.
$W=Fs$
$W=1N\times 5m=5J$