Work-energy-power practice · Medium

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

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

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

Force on a particle moving in straight line is given by $\vec{F}=6 t^2 \hat{i}-3 t \hat{j}$ and velocity is $\vec{v}=3 t^2 \hat{i}+6 t \hat{j}$. Find power at $t=2$.

Two springs with spring constants $k_1=1200 \mathrm{~N} / \mathrm{m}$ and $k_2=500 \mathrm{~N} / \mathrm{m}$ are stretched by the same force. The ratio of potential energy in the springs will be

A steel sphere of mass 100 gm moving with a velocity of 4 m/s collides with a dust particle elastically moving in the same direction with a velocity of 1 m/s. The velocity of the dust particle after the collision is

A ball $A$ moving with certain velocity along positive $x$-axis collides with a stationary ball $B$. After collision their directions of motion make angles $\alpha$ and $\beta$ with the $x$-axis. The possible values of $\alpha$ and $\beta$ are

A long spring when stretched by 2 cm its potential energy is $U$. If the same spring is stretched by 8 cm, then the potential energy of the spring is

Assertion(A): The relative velocity of the two particles in head on elastic collision is unchanged both in magnitude and direction.

Reason(R): The relative velocity is unchanged in magnitude but gets reversed in direction.

A force $\overrightarrow F = (\hat i + 2\hat j + 3\hat k)N$ displaces a particle from position $\overrightarrow {{r_1}} = (\hat i + \hat j + \hat k)m$ to position $\overrightarrow {{r_2}} = (\hat j + \hat k)m$. The work done by the force in doing so is

Statement-I: Work done by spring force on a block connected to the spring may be positive or negative.
Statement-II: Spring force is both pushing and pulling.

A body having weight $0.4 \mathrm{~kg}$ is whirled in a vertical circle with a string making 2 revolutions/second. Given that the radius of this circle is 1.2 $\mathrm{m}$. Find out the tension

(a) At the top of the circle

(b) At the lowermost point of the circle.

Given : $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$ and $\pi=3.14$.

Assertion (A): Graph between potential energy of a spring versus the extension or compression of the spring is parabola
Reason (R): Potential energy of a stretched or compressed spring proportional to square of extension or compression

Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement II Principle of conservation of momentum holds true for all kinds of collisions.

Assertion: If a body moving in a circular path has constant speed, then there is no force acting on it.
Reason: The direction of the velocity vector of a body moving in a circular path is changing.