Work-energy-power practice · Medium

Power applied to a particle varies with time as $P = \left( {3{t^2} - 2t + 1} \right)$ watt, where t is in second. Find the change in its kinetic energy between t=2 s and t=4 s

Assertion: A truck and a car moving with the same kinetic energy are brought to rest by the application of breaks which provide equal retarding forces. Both come to rest in equal distance.
Reason: It is possible that the speed of a body is zero but velocity is not zero.

In a circular motion of a body, which amongst the following relation between tangential acceleration and linear velocity is correct?

A body of mass $2 \mathrm{~kg}$ is projected vertically upwards with velocity $20 \mathrm{~m} / \mathrm{s}$. If the body rises to a height of $15 \mathrm{~m}$, the work done by air drag is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

Assertion (A): Work done by the gravitational force is zero, in closed path
Reason (R): Gravitational force is a conservative force

A particle is moving in a conservative force field from point $A$ to point $B . U_A$ and $U_B$ are the potential energies of the particle at points $A$ and $B$; and $W_C$ is the work done by conservative forces in the process of taking the particle from $A$ and $B$. Which of the following is true?

Assertion: The power of a pump which raises 100 kg of water in 10 sec to a height of 100 m is 10 KW.
Reason: The practical unit of power is horse power.

Three identical cars $A, B$ and $C$ are moving at the same speed on three bridges. The car $A$ goes on a plane bridge $B$ on a bridge convex upwards and $C$ goes on a bridge concave upwards. Let $F_A, F_B$ and $F_C$ be the normal forces exerted by the cars on the bridges when they are at the middle of the bridges. Then

A man does a given amount of work in 10 sec. Another man does the same amount of work in 20 sec. The ratio of the output power of first man to the second man is

In which of the following cases, can the work done increase the potential energy?

If a block of mass $M$ is moving with a velocity $v$ along a straight path, when a constant force is applied, its kinetic energy is $\frac{1}{2} M v^2$. Then

Assertion (A): No work is done by the centripetal force acting on a body moving along the circumference of a circle
Reason (R): At any instant, the motion of the body is along the tangent to the circle where as the centripetal force is along the radius vector towards the centre of the circle

A man carries a load of 50 kg through a height of 40 m in 25 seconds. If the power of the man is 1568 W, his mass is

A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is

Assertion: $\mathrm{KE}$ is conserved at every instant of (elastic) collision.

Reason: No deformation of matter occurs in elastic collision.

Statement-1: A block of mass ' $M$ ' is placed on a moving railroad car moving with velocity ' $v$ '. The kinetic energy of the block is $\frac{1}{2} M v^2$ in all frames.

Statement-2: The kinetic energy of a system or body is different in different frames.

Assertion: For uniform circular motion it is necessary that the speed of the particle is constant.
Reason: There is no tangential force or tangential acceleration acting on particle in uniform circular motion.

A metre stick of mass 400 gram is pivoted at one end and displaced through an angle ${60^0}$. The increase in its potential energy is

A rubber ball falls from a height and comes to rest after several rebounds on the horizontal ground. If $e = 0.5$ and the ball travels a total distance of 25 m, the height from which it fell down is

A small $0.500-\mathrm{kg}$ object moves on a frictionless horizontal table in a circular path of radius $1.00 \mathrm{~m}$. The angular speed is $6.28 \mathrm{~rad} / \mathrm{s}$. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than $1280 \mathrm{~N}$, what is the radius of the smallest possible circle (in $\mathrm{cm}$) on which the object can move?

In an inelastic collision

According to work-energy theorem, the work done by the net force on a particle is equal to the change in its

A particle moving along a circular path the radial acceleration ${a}_{{r}}$ is proportional to time $t$. if ${a}_{{t}}$ is the tangential acceleration, then which of the following will be independent of time $t?$

The potential energy of a system increases if work is done

A body is moving in a circular path with a constant speed. It has

A car moves on a circular road. It describes equal angles about the centre is equal intervals of time. Which of the following statements about the velocity of the car is true?

A particle of mass ${m}$ is rotating by means of a string in a vertical circle. The difference in the tension at the bottom and top would be-

Assertion: A person working on a horizontal road with a load on his head does no work.
Reason: No work is said to be done, if directions of force and displacement of load are perpendicular to each other.

The potential energy of a particle of mass $1 \mathrm{~kg}$ is $U=10+(x-2)^2$. Here, $U$ is in joule and $x$ in metre on the positive $X$-axis. Particle travels upto $x=+6 \mathrm{~m}$. Choose the correct option.

You accidentally bump into a bookcase. It tilts briefly but then returns to upright, and you breathe a sigh of relief. When you first bumped the bookcase, its center of gravity moved