Question

The force on a particle is directed along an $x$ axis and given by
$F=F_0(x/x_0-1).$ Find the work done by the force in moving the particle from $x=0$ to $x=2x_0$.

• A. $2x_0(F_0-1)$
• B. $x_0(F_0-1)$
• C. $3x_0(F_0-1)$
• D. $0$

Answer 1

The correct option is D $0$

Work done by a variable force is given by,
$W={\int }^{}Fdx$
$W=\int \frac{F_{0}xdx}{x_0}-\int F_{0}dx$

Here, the limits are from 0 to $2x_0$.
So after integrating we get,
$W=2F_0{x}_0-2F_0{x}_0=0$