Question

Potential energy of a particle is given by $U=(2-3x-4x^2)\text{J}$ where '$x$' is in '$m$'. Find the magnitude of force at $x=4\text{m}$, if the particle is free to move along $x$-direction.

• A. $29\text{N}$
• B. $35\text{N}$
• C. $16\text{N}$
• D. $18\text{N}$

Answer 1

The correct option is B $35\text{N}$

We know that, If the potential energy function $U\left(x\right)$ is known, then the force at any position can be obtained by taking the derivative of the potential

$\Rightarrow F=-\frac{\partial U}{\partial x}$
$=-\frac{\partial }{\partial x}(2-3x-4x^2)$
$=8x+3{|}_{x=4m}$
= $32+3$
$F=35\text{N}$

Hence option B is the correct answer