A small mass slides down an inclined plane of inclination $\mathrm{\theta }$ with the horizontal. The coefficient of friction is $\mathrm{\mu }={\mathrm{\mu }}_{\mathrm{o}}x$, where $x$ is the distance through which the mass slides down and ${\mathrm{\mu }}_{\mathrm{o}}$ a positive constant. Then the distance covered by the mass before it stops is

A toy car of mass $5 \mathrm{kg}$ starts from rest and moves up a ramp under the influence of force $F$($F$ is applied in the direction of velocity) plotted against displacement $x.$ The maximum height attained is given by

____________ of a two particle system depends only on the separation between the two particles.

The most appropriate choice for the blank space in the above sentence is

A block of mass $m$ is attached to two unstretched springs of spring constants $k_1$ and $k_2$ as shown in figure. The block is displaced towards right through a distance $x$ and is released. Find the speed of the block as it passes through the mean position shown.

A wedge of mass $M$ fitted with a spring of stiffness $\text{'}k\text{'}$ is kept on a smooth horizontal surface. A rod of mass $m$ is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all surfaces are smooth, the potential energy stored in the spring is :