Question

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

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

Answer 1

Answer: (C)

$\left(\frac{\sqrt{a^2+b^2}}{m}\right)$

For a conservative field, force $f=-▽V$ where V is the potential energy.

Now for gravitational potential U, force $F=▽U$

$F=\frac{\partial }{\partial x}(ax+by)\hat{i}+\frac{\partial }{\partial y}(ax+by)\hat{j}$

$m\overrightarrow{a}=a\hat{i}+b\hat{j}$

$⟹m|a|=\sqrt{a^2+b^2}$