Work-energy-power practice · Mixed difficulty

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.

Statement I: The centripetal force and the centrifugal force never cancel out.
Statement II: They do not act at the same time.

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

Keeping the angle of banking of the road constant, the maximum speed of the vehicles is to be increase by $10 \%$. The radius of curvature of the road will have to be changed from $20 {~m}$ to

A uniform force of 4 N acts on a body of mass 10 kg for a distance of 2.0 m. The kinetic energy acquired by the body is

Assertion: A body can have energy without having momentum.
Reason: A body can have momentum without having mechanical energy.

A force $F$ acting on a body depends on its displacement ${s}$ as $F \propto s^{-1 / 3}$. The power delivered by ${F}$ will depend on displacement as

Assertion: If ball is dropped from a higher altitude. There will be a greater value of impulse from ground during collision.
Reason: Gravity increases momentum of a ball.

Potential energy function along $x$-axis in a certain force field is given as $U(x)=\frac{x^4}{4}-2 x^3+\frac{11}{2} x^2-6 x$. For the given force field,

(i) the points of equilibrium are $x=1, x=2$ and $x=3$

(ii) the points $x=2$ is a point of unstable equilibrium

(iii) the points $x=1$ and $x=3$ are points of stable equilibrium

(iv) there exists no point of neutral equilibrium Which one of the following is the set of correct options?

Statement I: Work done in moving a body in non-uniform circular motion is zero.

Statement II: The centripetal force always acts along the radius of the circle.

Two bodies of masses $m$ and $2 m$ are moving along positive $x$ and $y$ axes respectively with equal speeds of $4 {~m} / {s}$. They collide at origin and stick together. The final velocity of combined mass is

Identify the correct statements from the following:

A. Work done by a man in lifting a bucket out of a well by means of rope tied to the bucket is negative.

B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.

C. Work done by friction on a body sliding down an inclined plane is positive.

D. Word done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.

E. Work done by the air resistance on an oscillating pendulum is negative.

Choose the correct answer from the options given below:

The ratio of angular speeds of the minutes hand and the hours hand of a watch is

A) When a ball hits a wall (stationary) it returns back with same velocity, if collision is elastic
B) A ball hits a bus moving towards it. If the collision is inelastic, they move together.
C) Inelastic collision arises due to loss in K.E during collision

A person holds a bucket of weight 60 N. He walks 7m along the horizontal path and then climbs up a vertical distance of 5 m. The work done by the man is

The potential energy of a body is given by

$U=40+6 x^2-7 x y+8 y^2+32 z$
where $U$ is in joule and $x, y, z$ in metre. Deduce the $x, y$ and $z$ components of the force (in newton) on the body when it is in position $(-2,0,+5)$

STATEMENT-1 : 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-2 : In an elastic collision, the linear momentum of the system is conserved.

A car when passes through a convex bridge exerts a force on it which is equal to