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 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…

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…

The potential energy of a system increases if work is done

A block of mass 1 kg slides down a curved track that is one quadrant of a circle of radius 1 m . Speed of the block at the bottom is $2 \mathrm{~m} / \mathrm{s}$. Work done by the frictional force on the block when it…

A fighter plane is moving in a vertical circle of radius $r$. Its minimum velocity at the highest point $A$ of the circle will be

Simple pendulum of length $l$ has a maximum angular displacement $\theta$. The maximum kinetic energy of the bob is

A metre scale is standing vertically on the earth's surface on one of its end. It now falls on earth without slipping. Find the velocity with which the free end of the scale strikes the earth. $\left(g=10 \mathrm{~m} /…

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30^{\circ}$ and $60^{\circ}$ from vertical (lowest positions) are $T_1$ and $T_2$, respectively. Then

A particle is projected from the surface of the earth with an initial speed of $4.0 \mathrm{kms}^{-1}$. The maximum height (in km) attained by the particle is _____ [Radius of earth $=6400 \mathrm{~km}$ and…

A particle which is constrained to move along the $x$-axis, is subjected to a force in the same direction which varies with the distance $x$ of the particle from the origin is $F(x)=-k x+a x^3$. Here, $k$ and $a$ are…