Question

A particle is placed in a field characterized by a value of gravitational potential given by $V=-kxy$, where k is a constant. If $\overline{E_g}$ is the gravitational field then.

• A. $\overline{E_g}=k(x\overline{i}+y\overline{j})$ and is conservative in nature
• B. $\overline{E_g}=k(y\overline{i}+x\overline{j})$ and is conservative in nature
• C. $\overline{E_g}=k(x\overline{i}+y\overline{j})$ and is non conservative in nature
• D. $\overline{E_g}=k(y\overline{i}+x\overline{j})$ and is non conservative in nature

Answer 1

The correct option is B $\overline{E_g}=k(y\overline{i}+x\overline{j})$ and is conservative in nature

$E=-\frac{dv}{dx}\overline{i}-\frac{dv}{dy}\overline{j}$

$E=ky\overline{i}+kx\overline{j}$

Gravitational field is conservative in nature.