An electric dipole is placed at an angle of $${30^ \circ }$$ to a non-uniform electric field. The dipole will experience

The potential energy of a $$1$$ $$kg$$ particle free to move along the $$x$$-axis is given by $$V\left( x \right) = \left( {{{{x^4}} \over 4} - {{{x^2}} \over 2}} \right)J$$.

The total mechanical energy of the particle is $$2J.$$ Then, the maximum speed (in $$m/s$$) is

Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed towards the center of mass through a distance $$d,$$ by what distance should the second particle is moved, so as to keep the center of mass at the same position?

A force of $$ - F\widehat k$$ acts on $$O,$$ the origin of the coordinate system. The torque about the point $$(1, -1)$$ is