Work-energy-power practice · Medium

Statement I: In an elastic collision of two billiards balls, the kinetic energy is not conserved during the short interval of time of collision between the balls.

Statement II: Energy spent against friction does not follow the law of conservation of energy.

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force is greatest

You lift a heavy book from the floor of the room and keep it in the book–shelf having a height 2 m. In this process you take 5 seconds. The work done by you will depend upon

Which of the following quantity is conserved in an elastic collision between two bodies during the collision?

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. If two springs $S_1$ and $S_2$ of the force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement-I: If stretched by the same amount, work done on $S_1$, will be more than that of $S_2$
Statement-II : $k_1 < k_2$

The force on a particle as the function of displacement ${x}$ (in ${x} /$ direction) is given by
${F}=10+0.5 {x}$

The work done corresponding to displacement of particle from ${x}=0$ to ${x}=2$ unit is

Assertion: Quick collisions are more violent than slow collisions.
Reason: Quick collision are inelastic in nature.

When a rubber band is stretched by a distance $x$, it exerts a restoring force of magnitude $F = ax + b{x^2},$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is

A particle of mass $m$ moves on a straight line with its velocity varying with the distance travelled according to the equation $v=\alpha x^{3 / 2}$, where $\alpha$ is a constant. The total work done by all the forces during a displacement from $x=0$ to $x=b$ is;

Assertion (A)In an elastic collision between two bides, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Reason (R) In elastic collision, the linear momentum of the system is conserved.

A ball of mass m moves with speed v and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is

Assertion: A car moving on a horizontal road may be thrown out of the road in taking a turn due to lack of proper centripetal force.
Reason: If a particle moves in a circle, describing equal angles in equal intervals of time. Then the velocity vector changes its magnitude.

A bullet of mass 10 Gm strikes a target at 400 m/s velocity and loses half of its initial velocity. The loss of kinetic energy in joules is

A car travelling at a speed of $30 {~km} / {hour}$ is brought to a halt in $8 {~m}$ by applying brakes. If the same car is travelling at $60 {~km} / {hour}$, it can be brought to a halt with the same braking force in

The bob of a simple pendulum having length $2 \mathrm{~m}$, is displaced from mean position to an angular position $\theta$ from vertical. If it is released, then velocity of bob at lowest position will be

Assertion: Kinetic energy of a body becomes four times, when its linear momentum is doubled.
Reason: This is because, $\mathrm{K.E.}=p^2 / 2 \mathrm{~m}$.

The bodies of masses 1 kg and 5 kg are dropped gently from the top of a tower. At a point 20 cm from the ground, both the bodies will have the same

The length of a steel wire increases by $0.5 \mathrm{~cm}$ when it is loaded with a weight of $5 \mathrm{~kg}$. Calculate force constant of the wire.

Statement-I: The work done by all forces on a system equals to the change in kinetic energy of that system. This statement is true even if non-conservative forces act on the system.
Statement-II: The total work done by internal forces may be positive.

Water is flowing in a river at $2 \mathrm{~ms}^{-1}$. The river is $50 \mathrm{~m}$ wide and has an average depth of $5 \mathrm{~m}$. The power available from the current in the river is: (Density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$)

A neutron in a nuclear reactor collides head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is

Statement-I: The normal force on a body by the floor is not a conservative force
Statement-II: The normal force does no work at all. Hence it will not store energy in the system.

Statement-1: A particle moving at constant speed and constant magnitude of radial acceleration not be undergoing uniform circular motion.
Statement-2: In uniform circular motion speed cannot change as their is no tangential acceleration.

In unloading grain from the hold of a ship, an elevator lifts the grain through a distance of $12 \mathrm{~m}$. Grain is discharged at the top of the elevator at a rate of $2.0 \mathrm{~kg}$ each second and the discharge speed of each grain particle is $3.0 \mathrm{~m} \mathrm{~s}^{-1}$. Find the minimum horsepower of motor that can elevate grain in this way.

A gun fires a small bullet with kinetic energy $K$. Then kinetic energy of the gun while recoiling is

A particle moves in a potential energy region given as $U=x^2-14 x+12$. Its state of equilibrium will be-

A body tied at the end of a string of length $' l '$ is rotated in a vertical circle. The velocity of the body at the highest point is $\sqrt{2 g l}$. The maximum velocity of the body would be

A box of mass $m$ is initially at rest on a horizontal surface. A constant horizontal force of ${mg} / 2$ is applied to the box directed to the right. The coefficient of friction of the surface changes with the distance pushed as $m=m_0 x$ where $x$ is the distance from the initial location. For what distance is the box pushed until it comes to rest again?

If the speed of a vehicle is increased by $1 \mathrm{~ms}^{-1}$, its kinetic energy is doubled, then original speed of the vehicle is

Which of the following is not a perfectly inelastic collision