Question

The potential energy of a body of mass $m$ is $U=ax+by$ . The magnitude of the acceleration of the body will be

• A. $\frac{ab}{m}$
• B. $\left(\frac{a+b}{m}\right)$
• C. $\frac{\sqrt{a^2+b^2}}{m}$
• D. $\frac{a^2+b^2}{m}$

Answer 1

Answer: (C)

We know that $U=ax+by$
$\frac{\partial U}{\partial x}=\frac{\partial }{\partial x}\left(ax+by\right)$
$\frac{\partial U}{\partial x}=a$
$\frac{\partial U}{\partial y}=\frac{\partial }{\partial y}\left(ax+by\right)$
$\frac{\partial U}{\partial y}=b$
$\overrightarrow{F}=\left(\frac{\partial U}{\partial x}\hat{i}+\frac{\partial U}{\partial y}\hat{j}\right)$
$\overrightarrow{F}=-a\hat{i}-b\hat{j}$
$F=\sqrt{a^2+b^2}$