Question

A particle is acted by a force F = kx, where k is a positive constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We know that $\Delta U=-W$ for conservative forces
$\therefore \Delta U=-{\int }_0^{x}Fdx=-{\int }_0^{x}Kxdx$
$\Rightarrow U_{\left(x\right)}-U_{\left(0\right)}=-\frac{k{x}^2}{2}$
$Given{U}_{\left(0\right)}=0\therefore U_{\left(x\right)}=-\frac{k{x}^2}{2}$