Work Power and Energy

A ball whose kinetic energy E, is projected at an angle of $45^\circ$ to the horizontal. The kinetic energy of the ball at the highest point of its height will be

If a body looses half of its velocity on penetrating $3$ $cm$ in a wooden block, then how much will it penetrate more before coming to rest?

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200N$ to the lower end. The weight stretches the wire by $1$ $mm.$ Then the elastic energy stored in the wire is

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

A uniform chain of length $2$ $m$ is kept on a table such that a length of $60$ $cm$ hangs freely from the edge of the table. The total mass of the chain is $4$ $kg.$ What is the work done in pulling the entire chain on the table?

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that

A bullet fired into a fixed target loses half of its velocity after penetrating $3$ $cm.$ How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

The upper half of an inclined plane with inclination $\phi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

A spherical ball of mass $20$ $kg$ is stationary at the top of a hill of height $100$ $m$. It rolls down a smooth surface to the ground, then climbs up another hill of height $30$ $m$ and finally rolls down to a horizontal base at a height of $20$ $m$ above the ground. The velocity attained by the ball is

A mass of $M$ $kg$ is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of ${45^ \circ }$ with the initial vertical direction is

A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -

A ball of mass $0.2$ $kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2$ $m$ while applying the force and the ball goes upto $2$ $m$ height further, find the magnitude of the force. (consider $g = 10\,m/{s^2}$).

A particle of mass $100g$ is thrown vertically upwards with a speed of $5$ $m/s$. The work done by the force of gravity during the time the particle goes up is

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

A particle is projected at $60^\circ$ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

A $2$ $kg$ block slides on a horizontal floor with a speed of $4m/s.$ It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is $15N$ and spring constant is $10, 000$ $N/m.$ The spring compresses by

An athlete in the olympic games covers a distance of $100$ $m$ in $10$ $s.$ His kinetic energy can be estimated to be in the range

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left( x \right) = {a \over {{x^{12}}}} - {b \over {{x^6}}},$ where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = \left[ {U\left( {x = \infty } \right) - {U_{at\,\,equilibrium}}} \right],\,\,D$ is

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements. If two springs ${S_1}$ and ${S_2}$ of force constants ${k_1}$ and ${k_2}$, respectively, are stretched by the same force, it is found that more work is done on spring ${S_1}$ than on spring ${S_2}$. STATEMENT 1: If stretched by the same amount work done on ${S_1}$, Work done on ${S_1}$ is more than ${S_2}$ STATEMENT 2: ${k_1} < {k_2}$