Work-energy-power practice · Mixed difficulty

The bob of a pendulum of mass m and length L is displaced, ${90^0}$ from the vertical and gently released. In order that the string may not break upon passing through the lowest point, its minimum strength must be

If coefficient of restitution for collision between two marble balls is equal to $\frac{1}{2}$, then the collision between them is

A force $\left( {4\hat i + \hat j - 2\hat k} \right)N$ acting on a body maintains its velocity at $\left( {2\hat i + 2\hat j + 3\hat k} \right)m{s^{ - 1}}$. The power exerted is:-

The angle between the linear momentum and angular momentum of particle moving along a circle is

A bullet is fired from a rifle. If the riffle recoils freely, then the kinetic energy of the rifle is

One object of mass $20 \mathrm{~kg}$ is moving with speed $10 \mathrm{~ms}^{-1}$ in west direction and another object of mass $10 \mathrm{~kg}$ is moving with $15 \mathrm{~ms}^{-1}$ in north direction. Both collide and stick together. Choose the correct alternative.

The maximum and minimum tensions in the string whirling in a circle of radius 2.5 m are in the ratio 5:3, then its velocity is

Assertion : In an elastic collision of two bodies, the momentum and energy of each body is conserved.
Reason : If two bodies stick to each other, after colliding, the collision is said to be perfectly elastic.

If ${a_r}\,and\,{a_t}$ represent radial and tangential accelerations, the motion of a particle will be uniformly circular if

A particle moves along a curve of unknown shape but magnitude of force $\vec{F}$ is constant and always acts along the tangent to the curve. Then,

Statement-A: Energy is the cause for doing work and work is the effeet
Statement-B: Energy is a scalar but power is a vector quantity.

A block of mass ${m}=0.5 \mathrm{~kg}$ gently placed on a conveyor belt moving with velocity of $4 \mathrm{~m} / \mathrm{s}$. The coefficient of friction between the conveyor belt and bag is $0.2.$ Initially the block slips on the conveyor belt before it stops due to friction. The work done by kinetic friction on the block is $\left[{g}=10 \mathrm{~m} / \mathrm{s}^2\right]$

The turbine pits at the Niagra falls are $50 \mathrm{~m}$ deep. The average horse power developed is 500. If the efficiency of the generator is $85 \%$, how much water passes through the turbines per minute? Take $g=10 \mathrm{~ms}^{-2}$.

Two substances have masses $90 \mathrm{~kg}$ and $160 \mathrm{~kg}$ respectively. They possess equal kinetic energy. The ratio of their momenta will be

A force of constant magnitude $F=10 \mathrm{~N}$ acts on a particle moving in a plane such that it is perpendicular to the velocity $\vec{v}(|\vec{v}|=v=5 \mathrm{~m} / \mathrm{s})$ of the body, and the force is always directed towards a fixed point. Then the angle (in radian) turned by the velocity vector of the particle as it covers a distance $S=10 \mathrm{~m}$ is (take: mass of the particle as $m=2 \mathrm{~kg})$

A bullet fired from a gun can pierce a target due to its:

A groove is in the form of a broken line $A B C$ and the position vectors of the three points are respectively $2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. A force of magnitude $24 \sqrt{3}$ acts on a particle of unit mass kept at the point $A$ and moves it along the groove to the point $C$. If the line of action of the force is parallel to the vector $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ all along, the number of units of work done by the force is

Two moving particles collide and stick together on a smooth horizontal surface. The following statements are given below

(a) Mechanical energy is conserved.

(b) Total energy is conserved.

(c) Work done by the system is positive

(d) Work done by the system is negative.

Choose the correct option.

A 2kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad / sec. If radius of path becomes 1 M, then the value of angular velocity will be [rad / sec]

The displacement x in metre of a particle of mass m kg moving in one dimension under the action of a force is related to the time t in second by the equation $t = \sqrt x + 3$, the work done by the force (in joule) in first six seconds is

A mass of $1 \mathrm{~kg}$ is acted upon by a single force ${F}=(4 \hat{{i}}+4 \hat{j}) \mathrm{N}$. Under this force, it is displaced from $(0,0)$ to $(1 \mathrm{~m}, 1 \mathrm{~m})$. If initially, the speed of the particle was $2 \mathrm{~ms}^{-1}$, its final speed should be

If $n$ bullets each of mass $m$ are fired with a velocity $v$ per second from a machine gun, the force required to hold the gun in position is

A body of mass 6 kg is acted upon by a force which causes a displacement in it given by $x\frac{{{t^2}}}{{4\;}}\;\;$ metre where t is the time in second. The work done by the force in 2s is

A ball of mass $m$ collides with a wall with speed $v$
and rebounds on the same line with the same
speed. If mass of the wall is taken infinite at rest,
then work done by the ball on the wall is

A ball of mass 0.1 kg is suspended by a string. It is displaced through an angle of ${60^0}$ and left. When the ball passes through the mean position, the tension in the string is

An engine accelerates a car of mass 800 kg to a speed of $72\mathrm{\;km}{\mathrm{h}^{ - 1}}$. If the frictional force is 10 M per ton, the power developed by the engine is

The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be

Assertion: The gain in potential energy of an object of mass $m$ raised to height equal to the radius of earth is $\frac{1}{2} \mathrm{~mgR}$.
Reason: Kinetic energy at surface $\frac{1}{2} m v^2=$ P.E at the top and at the top, $v=\sqrt{g R}$.

$\therefore \mathrm{PE}=\frac{1}{2} \mathrm{~mgR}$

Assertion (A): When a body moving with certain velocity collides head on with another body of same mass at rest, the collision being perfectly elastic head on collision, $100 \%$ of its K.E is transferred to the later
Reason (R): Both momentum and KE are conserved in the case of perfectly elastic collision

In a nuclear reactor, the fuel is consumed at the rate of 1 mg/s. The power generated in kilowatt is