Work-energy-power practice · Medium

A particle moves in a circle of radius $r$ under the action of a centripetal force equal to $-\frac{k}{r^2} \hat{r}$, where $k$ is a constant. The total energy of the particle is

Which of the following is true:

Statement A: A particle is moving with constant speed must have constant velocity also.

Statement B: If velocity of a particle is zero then its acceleration may not be zero.

Statement I: The tendency to overturn of skidding/overturning is quadrupled, when a cyclist doubles his speed of turning.

Statement II: $\tan \theta=\frac{\mathrm{v}^2}{\mathrm{Rg}} \Rightarrow$ becomes 4 times as $v$ doubled.

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? $(g = 10\mathrm{ m/}{\mathrm{s}^2})$

A time t=0 s Particle starts moving along the x-axis. If its kinetic energy increases uniformly with time t, the net force acting on it must be proportional to

A body of mass $1 \mathrm{~kg}$ is rotated in a horizontal circle of radius $1 \mathrm{~m}$ and moves with velocity $2 \mathrm{~m} / \mathrm{sec}$. The work done in 10 revolutions is

A force $\vec{F}=\hat{i}+5 \hat{j}+7 \hat{k}$ acts on a particle and displaces it through $\vec{s}=6 \hat{i}+9 \hat{k}$. Calculate the work done if the force is in newton and displacement in metre.

A quarter horse power motor runs at a speed of 600 r.p.m. Assuming 40% efficiency the work done by the motor in one rotation will be

A body starts from rest and acquires a velocity $V$ in time $T$. The work done on the body in time $t$ will be proportional to

Kinetic energy of a particle moving in a straight line varies with time $t$ as $K=4 t^2$. The force acting on the particle

The potential energy of a body as a function of distance is given as $U(x)=\left(-6 x^2+2 x\right) {J}$. The conservative force acting on body at $x=1 {~m}$ will be

Assertion: The work done by the spring force in a cyclic process is zero.
Reason: Spring force is a conservative force.

A) Work done by frictional force is always negative
B) A body at rest can have mechanical energy
C) Mechanical energy of freely falling body decrease gradually

Maximum energy transfer for an elastic collision will occur if one body is at rest when

In uniform circular motion which of the following quantity is zero?

A $1 \mathrm{~kg}$ ball, moving at $12 \mathrm{~m} \mathrm{s}^{-1}$, collides head-on with a $2 \mathrm{~kg}$ ball moving in the opposite direction at $24 \mathrm{~m} \mathrm{s}^{-1}$. If the coefficient of restitution is $\frac{2}{3}$, then what is the energy lost in the collision?

At what time $\mathrm{PE}$ will be equal to half of the total energy (TE) :-

A body of mass $m$ is moving with a velocity $v_1.$ If a force $F$ acts on it and displaces it by $d,$ then final velocity will be

The potential energy of a particle of mass $3 {~kg}$ free to move along the $x$-axis is given by $U(x)=\left(\frac{3 x^2}{2}-2 x\right) {J}$. If total mechanical energy of the particle is $5 {~J}$, then the maximum speed of the particle is;

Water falls down a $500.0 \mathrm{~m}$ shaft to reach a turbine which generates electricity. How much water must fall per second in order to generate $1.00 \times 10^9 \mathrm{~W}$ of power?

(Assume 50% efficiency of conversion and $g=10 \mathrm{~ms}^{-2}$)

A body is moving in a vertical circle such that the velocity of body at lowest point is critical. The ratio of velocities of body at angular displacements ${60^0}$ and ${120^0}$ from lowest point is

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

The potential energy of a particle varies with x according to the relation $U\left( x \right) = {x^2} - 4x$ . The point x = 2 is a point of

Work done in raising a box depends on:

A force $(3 \hat{i}+\hat{j}-2 \hat{k}) \mathrm{N}$ acting on a body maintains its velocity at $(3 \hat{i}+3 \hat{j}+3 \hat{k}) \mathrm{ms}^{-1}$. The power exerted is

A particle of mass $\mathrm{m}_1$ collides head-on with another stationary particle of mass $\mathrm{m}_2\left(\mathrm{m}_2 > \mathrm{m}_1\right)$. The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

A car is moving along a circular path of radius $500 {~m}$ with a speed of $30 {~ms}^{-1}$. If at some instant, its speed increases at the rate of $2 {~ms}^{-1}$, then at that instant, the magnitude of resultant acceleration will be

A particle of mass $m$ collides head-on with another stationary particle of mass $M$ such that the second particle starts moving and the first particle comes to rest after the collision. Which of the following conditions is valid if the coefficient of restriction is $e$?

Statement-I: A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical.
Statement-II: The rate of change of momentum determines that the force is small or large.

A long spring, when stretched by x cm has a potential energy U. On increasing the length of spring by stretching to nx cm, the potential energy stored in the spring will be