Question

A particle is moving in a potential region given by $U=K(x^2+y^2+z^2)$. The force acting on the particle is given by:

• A. $-2K(x\hat{i}+y\hat{j}+z\hat{k})$
• B. $K(x\hat{i}+y\hat{j}+z\hat{k})$
• C. $\frac{K}{2}(x\hat{i}+y\hat{j}+z\hat{k})$
• D. $K(x^2\hat{i}+y^2\hat{j}+z^2\hat{k})$

Answer 1

The correct option is A $-2K(x\hat{i}+y\hat{j}+z\hat{k})$

The relation between potential energy and force is given by,
$\overrightarrow{F}=-(\frac{\partial U}{\partial x}\hat{i}+\frac{\partial U}{\partial x}\hat{j}+\frac{\partial U}{\partial x}\hat{k})$
Putting the value of U in the above equation will get,
$\overrightarrow{F}=-2K(x\hat{i}+y\hat{j}+z\hat{k})$