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. $\frac{a b}{m}$
• 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 $U=ax+by$
$\frac{\partial U}{\partial x}=\frac{\partial}{\partial x}\left(a x + b y\right)$
$\frac{\partial U}{\partial x}=a$
$\frac{\partial U}{\partial y}=\frac{\partial}{\partial y}\left(a x + b y\right)$
$\frac{\partial U}{\partial y}=b$
$\overset{ \rightarrow }{F}=\left(\frac{\partial U}{\partial x} \hat{i} + \frac{\partial U}{\partial y} \hat{j}\right)$
$\overset{ \rightarrow }{F}=-a\hat{i}-b\hat{j}$
$F=\sqrt{a^{2} + b^{2}}$