Work-energy-power practice · Mixed difficulty

Statement-1: Work done by conservative force along closed path is zero.
Statement-2: When an object is moved along closed path beginning and ending at same point its displacement is zero.

A bucket full of water weighs 5 kg, it is pulled from a well 20 m deep. There is a small hole in the bucket through which water leaks at a constant rate of $0.2kg{m^{ - 1}}$ .The total work done in pulling the bucket up from the well is ($g = 10m{s^{ - 2}})$

The work done in pulling up a block of iron weighting 2 KN with a constant velocity through a distance of 10 m on a smooth inclined at an angle of $30^\circ$ with the horizontal is $\left[ {g = 10\,\,\,{\text{m}}{{\text{s}}^{ - 2}}} \right]$

If the momentum of a body is increased by 50% then the percentage increase in its kinetic energy is

Statement I Two bodies of different masses have the same momentum, and their kinetic energies are in the inverse ratio of their masses.

Statement II Kinetic energy of body is given by the relation.

${KE}=\frac{1}{2} m v^2$

Consider the following statements. A and B and identify the correct answer given below. I. Body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time. II. When a body is at rest, it must be in equilibrium.

A marble going at a speed of $2\,\,m/s$ hits another marble of equal mass at rest. If the collision is perfectly elastic, then the velocity of the first marble after collision is $\left( {in\,\,m/s} \right)$

The tension in the string revolving in a vertical circle with a mass m at the end which is the lowest position

If momentum will increase by $0.3 \%$ and mass will decrease by $0.2 \%$, then find out percentage change in kinetic energy.

Two bodies A and B of definite shape (dimensions of bodies are not ignored). A is moving with speed of 10 $\mathrm{m}{\mathrm{s}^{ - 1}}$ and B is in rest, collide elastically. The

Assertion (A): The change in kinetic energy of a particle is equal to work done on it by the resultant force.
Reason (R): Change in kinetic energy is equal to work done in case of system of one particle.

For a particle in non-uniform accelerated circular motion

A man cycles up a hill, whose slope is 1 in 20 with a velocity of $6.4 \mathrm{~kmh}^{-1}$ along the hill. The weight of the man and the cycle is $98 \mathrm{~kg}$. What work per minute is he doing? What is his horse power?

Assertion (A): No work is done by gravitational force if a body moves along a horizontal surface.
Reason (R): In horizontal motion, angle between gravity and displacement is $90^{\circ}$

A ball is allowed to fall from a height of 10 m. If there is 40% loss of energy due to impact, then after one impact ball will go up to

A bullet of mass 25 g moving with velocity of 400 m/s enters into a wooden block and comes out of it with a velocity of 100 m/s. Find the work done by the bullet while passing through the wooden block.

The power of a water pump is 200 kW. If $\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}$, then the amount of water it can raise in 1 min to a height of 10 m is

In position $A$, kinetic energy of a particle is $60 \mathrm{~J}$ and potential energy is $-20 \mathrm{~J}$. In position $B$, kinetic energy is $100 \mathrm{~J}$ and potential energy is $40 \mathrm{~J}$. Choose the correct statement, if the particle moves from $A$ to $B$.

If $v, p$ and $E$ denote velocity, linear momentum and kinetic energy of the particle respectively, then

In an elastic collision of two particles, the
following is conserved

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. [Take, $g = 9.8\,m{s^{ - 2}}$]

The slope of the kinetic energy displacement curve of a particle in motion is

A motor is used to deliver water at a certain rate from a given pipe. To obtain 3 times water from same pipe in same time, by what factor should power of the motor be increased.

If the radius of curvature of the path of two particles of same mass are in the ratio $3: 4$, then in order to have constant centripetal force, their velocities will be in the ratio of :

An electric pump is used to fill an overhead tank of capacity $8 \mathrm{~m}^3$ kept at a height of $10 \mathrm{~m}$ above the ground. If the pump takes 4 minutes to fill the tank by consuming $10 \mathrm{~kW}$ power, the efficiency of the pump should be

(Take $g=10 \mathrm{~m} \mathrm{s}^{-2}$ )

An electron of mass $9.0 \times 10^{-28} \mathrm{~g}$ is moving at a speed of $1000 \mathrm{~m} / \mathrm{sec}$. Calculate its kinetic energy if the electron takes up this speed after moving a distance of $10 \mathrm{~cm}$ from rest. Also calculate the force in $\mathrm{kg}$ weight acting on it.

A block having mass $m$ collides with an another stationary block having mass $2 \mathrm{~m}$. The lighter block comes to rest after collision. If the velocity of first block is $v$, then the value of coefficient of restitution will must be

The net work done by kinetic friction

A free body of mass 8 kg is travelling at 2 meter per second in a straight line. At a certain instant, the body splits into two equal parts due to internal explosion which releases 16 joules of energy. Neither part leaves the original line of motion finally, then

When a body moves with a constant speed along a circle