Question

A body is acted upon by a force that is proportional to the distance covered. If the distance covered is denoted by x, then work done by the force will be proportional to :

• A. $x$
• B. $x^2$
• C. $x^{\frac{3}{2}}$
• D. $x^4$

Answer 1

The correct option is B $x^2$

Given : $\text{The force is proportional to the displacement}$

$\therefore F\propto x\Rightarrow F=kx$

We know that $\text{Work done}\left(W\right)=F.x$

$\therefore W=Fx=k.x.x=k{x}^2$

So, $W\propto x^2$