Work Power Energy

A particle is whirled in a vertical circle of radius $R$. If its velocity at the lowest point is just enough to complete the circle ($u = \sqrt{5gR}$), then the magnitude of its total acceleration when the string…

The spring is initially in an equilibrium condition. Initially it is stretched by length $l$ and the work done is $U_1$. Again, it is stretched by length $\dfrac{7l}{2}$, when the work done is $U_2$, the value of $U_2$…

A ball is thrown vertically downwards from a height of $30$ m with initial velocity $V_0$. It collides with the ground and losses $60\ \%$ of its energy in collision rebounds to $20$ m. The initial velocity $V_0$ is ($g…

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling…

The potential energy of a system increases if work is done

The relationship between the force $F$ and position $x$ of a body is as shown in the figure. The work done in displacing the body from $x=1 \mathrm{~m}$ to $x=5 \mathrm{~m}$ will be

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $AB=D$. The height $h$ is equal to,

A mass of $1\mathrm{kg}$ falls from a height of $1m$ and lands on a mass less platform supported by a spring having spring constant $15Nm^{-1}$ as shown in the figure. The maximum compression of the spring is.…

A small disc of mass $m$ slides down with initial velocity zero from the top $(A)$ of a smooth hill of height $H$ having a horizontal portion $(B C)$ as shown in the figure. If the height of the horizontal portion of…

A ball of mass $10 \mathrm{~g}$ is allowed to fall down from 10 $\mathrm{m}$ height. After collision with the ground if $50 \%$ of its energy is lost, then the height reached by the ball is

A particle slides down along an inclined plane $A C$. If the plane is frictionless, kinetic energy of particle at $C$ is

A block of mass $m=25 \mathrm{~kg}$ sliding on a smooth horizontal surface with a velocity $v=3 \mathrm{~ms}^{-1}$ meets the spring of spring constant $k=100 \mathrm{~N} / \mathrm{m}$ fixed at one end as shown in…