Work-energy-power practice · Medium

For a body in uniform circular motion, the

Statement I In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Statement II Inan elastic collision, the linear momentum of the system is conserved.

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

I. Spring force is a conservative force.

II. Potential energy is defined only for conservative forces.

A simple pendulum is oscillating with an angular amplitude ${60^0}$. If mass of bob is 50 gm, then the tension in the string at mean position (in N) is $\left( {\mathrm{g = 10}\,\,\mathrm{m/}{\mathrm{s}^\mathrm{2}}} \right)$

Find W.D in stretching a storing of spring constant $\mathrm{K}$ from extension $x_0$ to extension $3 x_0$ ?

A body of mass m kg is lifted by a man to a height of one metre in 30 sec. Another man lifts the same mass to the same height in 60 sec. The work done by them are in the ratio

A particle of mass 100 gm moves in a potential well given by $U=8 x^2-4 x+400$ Joule. Find its acceleration at a distance of $25 \mathrm{~cm}$ from equilibrium in the positive direction

Two identical spheres move in opposite directions with speeds $v_1$ and $v_2$ and pass behind an opaque screen where they may either cross without touching (event 1 ) or make an elastic head-on collision (event 2) -

A person with a mass of $M \mathrm{~kg}$ stands in contact against the wall of a cylindrical drum of radius $r$ rotating with an angular velocity $\omega$. If the coefficient of friction between the wall and the clothing is $\mu$, the minimum rotational speed of the cylinder which enables the person to remain stuck to the wall when the floor is suddenly removed, is

A constant power p is applied to a car starting from rest. If v is the velocity of the car at time t, then

A ball of mass ${m_1}$ is a moving with velocity $v$. It collides head on elastically with a stationary ball of mass ${m_2}$. The velocity of ball becomes v/3 after collision. Then the value of the ratio $\frac{{{m_2}}}{{{m_1}}}$ is

A) For any collision, momentum transfer takes place.
B) In any collision, energy transfer takes place.
C) Impulsive forces are involved in collisions.

Assertion: Uniform circular motion is always an accelerated motion.
Reason: Direction of acceleration is parallel to the velocity vector.

Statement I A cyclist is moving on an unbanked road with a speed of $7\,km{h^{ - 1}}$ and takes a sharp circular turn along a path of radius of 2 m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve $\left( {g\, = \,9.8\,m/{s^2}} \right)$
Statement II If the road is banked at an angle of ${45^\mathrm{o}}$, cyclist can cross the curve of 2 m radius with the speed of $18.5\,km{h^{ - 1}}$ without slipping.
In the light of the above statements, choose the correct answer from the options given below.

Motion of a particle in $x - y$ plane is described by a set of following equations $x = 4\sin \left( {\frac{\pi }{2} - \omega t} \right)m$ and $y = 4\sin \left( {\omega t} \right)m.$ The path of the particle will be

A man pushes a wall and falls to displace it. He does

One end of string of length $l$ is connected to a particle of mass $'m'$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed $'v',$ the net force on the particle (directed towards center) will be ( $T$ represents the tension in the string)

Velocity of a particle of mass $4 \mathrm{~kg}$ moving along $\mathrm{x}$-axis is given as ${v}=2({x})^{3 / 2}$ then work done by forces acting on the particle when it moves from ${x}=0$ to ${x}=2 \mathrm{~m}$ is :-

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{{m{v^2}}}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

A simple pendulum is oscillating with an angular amplitude ${60^0}$. If mass of bob is 50 gm, then the tension in the string at mean position (in N) is $\left( {\mathrm{g = 10}\,\,\mathrm{m/}{\mathrm{s}^\mathrm{2}}} \right)$

The speed of a particle moving in a circle is increasing. The dot product of its acceleration and velocity is

A body is travelling in a circle at a constant speed. It

Power delivered to a particle varies with time as $P=\left(3 t^2-2 t\right)$ watt, where ' $t$ ' is in seconds, then change in its kinetic energy between time $t=1$ to $t=3 \mathrm{~s}$.

When a body slides against a rough horizontal surface, the work done by friction is:

Consider a car moving on a straight road with a speed of $60 \mathrm{~m} / \mathrm{s}$. If the engine is switched off then the distance affer which car will be stopped is $[\mu_{k}=0.4]$

A ball moving horizontally with a velocity of $2 \mathrm{~ms}^{-1}$ strikes the bob of a seconds pendulum at rest. If the mass of the bob is equal to the mass of the ball and the collision is perfectly elastic, after collision the bob of the pendulum will raise to a height of ($g=10 \mathrm{~ms}^{-{2}}$)

A force of 1200 N acting on a stone by means of rope slides the stone through a distance of 10 m in a direction inclined at ${60^0}$ to the force. The work done by the force is [Joules].

A body is tided with a string and is given a circular motion with velocity v in radius r. The magnitude of the acceleration

A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass on hitting the wall rebounds with the same speed. It can be concluded that

The centripetal acceleration of a particle varies inversely with the square of the radius rof the circular path .The KE of this particle varies directly as