Work-energy-power practice · Mixed difficulty

If ratio of centripetal acceleration of two particles moving on the same path is $3: 4$. Find the ratio of their tangential velocities.

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F=\frac{K}{v}$. Here $K$ is constant. The work done by this force in time $t$ is

Sand is falling on a conveyor belt at the rate of $5\,kg\,{s^{ - 1}}$. The extra power required to move the belt with a velocity of $6\,m{s^{ - 1}}$ is

A body slides down a frictionless track which ends in a circular loop of diameter D. Then the minimum height h of the body in terms of D so that it may just complete the loop, is

A bullet of mass $20 \mathrm{~g}$ moving with $600 \mathrm{~ms}^{-1}$ collides with a block of mass $4 \mathrm{~kg}$ hanging with the string of length $0.4 \mathrm{~m}$. What is velocity of bullet when it comes out of block, if block rises to height $0.2 \mathrm{~m}$ after collision? (Take, $g=10 \mathrm{~ms}^{-2}$ )

Which among the following is a form of energy

The string of a pendulum of length l is displaced through ${90^0}$ from the vertical and released. Then the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is

When a simple pendulum is rotated in a vertical plane with constant angular velocity, centripetal force is

Assertion: When a force of 20 N displaces a body by 5 m then work done by this force must be 100 J for every observer watching that body.
Reason: Work done on a body does not depend on the observer that is observing the body.

A spring when stretched by 2 mm its potential energy becomes 4 J. If it is stretched by 10 mm, its potential energy is equal to

Assertion: During horizontal circular turn of a car, the centripetal force required should be less than
the limiting friction between its tyres and road.

Reason: The centripetal force to car is provided by the frictional force between its tyres and road.

The power of a water jet flowing through an orifice of radius r with velocity v is

Angle between position vector and acceleration vector of a particle in uniform circular motion (centre of circle is taken as origin) is

Consider the following two statements 1. Linear momentum of a system of particles is zero 2. Kinetic energy of a system of particles is zero, Then

Potential energy is also called as

Statement-I: In circular motion, the centripetal and centrifugal force acting in opposite direction balance each other.
Statement-II: Centripetal and centrifugal forces don't act at the same time.

A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by $2\mathrm{\;m}{\mathrm{s}^{ - 1}}$ and the boy changes his speed by $x = \mathrm{m}{\mathrm{s}^{ - 1}}$, so that the kinetic energies of the boy and the man are again equal. Then x in $\mathrm{m}{\mathrm{s}^{ - 1}}$ is

A force $\vec{F}=\frac{-k}{x^2} \hat{i}(x \neq 0)$ acts on a particle moving in $x$-direction. The work done by this force in displacing a particle from $x=+a$ to $x=+2 a$ ( $k=$ Positive constant) is equal to

If the engine power is $3.3 \mathrm{~kW}$ and it is $60 \%$ efficient, how much water will it pump in $5 \mathrm{~s}$ from a height of $10 \mathrm{~m}$ ?

Statement-1: Linear momentum is conserved only during an elastic collision between two finite particles
Statement-2: The collision is infact a redistribution of the total momentum of the particles.

Consider a one-dimensional motion of a particle with total energy $E$. There are four regions $A, B, C$ and $D$ in which the relation between potential energy $V$, kinetic energy $K$ and total energy $E$ is as given below:

Region $A: V > E$

Region $B: V < E$

Region $C: K > E$

Region $D: V > K$

Which of the following regions the particle cannot be found?

Assertion: Kinetic energy is conserved in both, perfectly elastic & inelastic collisions.
Reason: Because both the types of collisions are identical.

A particle is moving in a circle of radius $r$ under the action of a force ${F}=\alpha {r}^2$ which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $=0$ for $r=0$):

Two bodies A and B have masses 2 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg wt. If they acquire the same kinetic energy in times ${t_A}\,and\,{t_B}$ , then the ratio$\frac{{{t_A}}}{{{t_B}}}$ is

I. In elastic collision, initial kinetic energy is equal to the final kinetic energy.
II. In elastic collision, kinetic energy during the collision time $\Delta t$ is constant.

Which of the following statement(s) is/are correct?

In which type of collision, the momentum of system is conserved?

A body of mass 2 kg moves down the quadrant of a circle of radius 4 m. If the velocity on reaching the lowest point is 8 m/s. The work done against friction is

The kinetic energy of a body is increased by $300\%$. What is the percentage increase in the momentum of the body?

The potential energy $U=3 a x^3-2 b x^2$. The force constant is represented by

Which of the following statements is/are true about the rotatory motion along a circular path?