Question

A particular force propels a particle in such a way that the force can be represented by the function $F\left(x\right)=\sin 2x$, where $x$ is in meters and $F$ is in Newtons (the proper conversion of input and output units and dimensions is implied).
When the particle moves from $x=\frac{\pi }{2}$ to $x=\pi$, by how much does its potential energy change?

• A. $2$
• B. $1$
• C. $0$
• D. $-1$
• E. $-2$

Answer 1

The correct option is B $1$

Potential energy changed in moving an object from $x_1$ to $x_2$ under a force $F=-{\int }_{x_1}^{x_2}Fdx$

Hence potential energy change caused here=$-{\int }_{\pi /2}^{\pi }sin2xdx$

$=\frac{cos2x}{2}{]}_{\pi /2}^{\pi }$

$=1$