Exrecise 2

There is a smooth fixed concave surface. A particle of mass $m$ Is released from $p.$ Find Kinetic energy as a function of $\theta$.

Radius of surface is. $R$

A $750 \mathrm{W}$ motor drives a pump which lifts $300$ litres of water per minute to a height of $6$ $\mathrm{m}$. The efficiency of the motor is nearly (take acceleration due to gravity to be $10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A body of $0.5 \mathrm{kg}$ moves along the positive $x$-axis under the influence of a varying force $F$ (in newton) as shown below:

If the speed of the object at $x=4 \mathrm{m}$ is $3.16 \mathrm{m} {\mathrm{s}}^{-1}$, then its speed at $x=8 \mathrm{m}$ is,

A block of mass $m$ is sliding down an inclined plane with constant speed. At a certain instant $t_0,$ its height above the ground is $h.$ The coefficient of kinetic friction between the block and the the plane is $\mu .$ If the block reaches the ground at a later instant $t_g,$ then the energy dissipated by friction in the time interval $\left(t_{\mathrm{g}}-t_0\right)$ is,

A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential $U\left(x\right)=\frac{x^4}{4}-\frac{x^2}{2} \mathrm{J}$, where $x$ is in meters. At time $t=0 \mathrm{s},$ it is at $x=-0.5 \mathrm{m}.$ Then at a later time it can be found,