Work Energy and Power

Under the action of a force F=cx, the position of a body changes from 0 to x.The work done is

A moving neutron collides with a stationary α-particle. The fraction of the kinetic energy lost by the neutron is

The momentum of a body is increased by 20%.The percentage increases in kinetic energy is

300j work is done in sliding a 2kg block up an inclined plane of height 10m.Taking g=10 ms⁻², work done against friction is

The potential energy of a system increases if work is done

A body of mass 10 kg is moving on an inclined plane of inclination 30°with an acceleration 2 ms⁻².The body starts from rest, the work done by the force of gravity in 2s is

A uniform force of (3i+j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2i+k)m to position (4i+3j-k)m.The work done by the force on the particle is

Three objects A,B and C are kept in a straight line on a frictionless horizontal surface.These have masses m,2m and m respectively.The object a moves towards b with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completly inelastic collision with C.All motions occur on the same straight line.Find the final speed (in m/s) of the object C

A body of mass (4m) is lying in xy plane at rest.It suddenly explodes into three pieces.Two pieces each of mass m move perpendicular to each other with equal speeds v.The total kinetic energy generated due to explosion is

A small block of super dense material has mass 3 x 10²⁴ kg.It is situated at a height h(<

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

A high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s.Time taken by the two radius vectors connecting point of explosion of fragments to make 90° is

A particle free to move along X-axis has potential energy given as U(X) = k(1-e-ˣ²), where k is a positive constant of appropriate dimension. Then, for -a < X < ∞

Assertion(A) :The change in kinetic energy of a particle is equal to the work done on it by the net force.
Reason(R) : Change in kinetic energy of a particle is equal to the work done only in case of a system of one particle

A particle of mass m is driven by a machine that delivers a constant power k watts.If the particle starts from rest the force on the particle at time t is

A particle moves along the x-axis from x=0 to x=5 m under the influence of a force given by F=7-2 x + 3x². The work done in the process is

A car moving with a speed of 50 kmh⁻¹ can be stopped by brakes after at least 6 m.If the same car is moving with 100 kmh⁻¹, the minimum stopping distance is

A block of mass 10 kg is moving in X-direction with a constant speed of 10 ms⁻¹.It is subjected to a retarding force F=-0.1 x m⁻¹, during its travel from x=20m to x=30m.Its final kinetic energy will be

A block of mass m moving at a velocity v collides with another block of mass 2m at rest.The lighter block comes to rest after collision.Find the coefficient of restitution.

A body of mass 0.5 kg travels in a straight line with velocity v=a x³/², where a= 5m⁻¹/² s⁻¹.The work done by the net force during its displacement from x=0 to x=2 m is

A block of mass 10 kg, moving in x-directions with a constant speed of 10 ms⁻¹, is subjected to a retarding force F=0.1x J/m during its travel from x=20 m to 30 m. Its final KE will be

A body of mass 1 kg is thrown upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (g = 10 m/s²)

A body of mass m is accelerated uniformly from rest to a speed v in a time T.The instantaneous power delivered to the body as a function of times is, given by

A bicyclist comes to a skidding stop in 10 m.During this process, the force on the bicycle due to the road is 200N and is directly opposed to the motion. The work done by the cycle on the road is

A train of mass 2x 10⁵ kg has a constant speed of 20 m/s up a hill inclined at θ= sin⁻¹(1/50) to the horizontal when the engine is working at 8 x 10⁵ W.The resistance to motion of train is

A bullet of mass m moving with velocity v strikes a block of mass M at rests and gets embedded into it .The kinetic energy of the composite block will be

The power supplied by a force acting on a particle moving in a straight line is constant.The velocity of the particle varies with displacement x as

When a bullet of mass 10 g and speed 100 ms⁻¹ penetrates up to distance 1cm in a human body in rest .The resistance offered by human body is

A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when

A spring of spring constant 5 x 10³ Nm⁻¹ is streched intially by 5 cm from the unstreched position.Then, the work required to strech it further by another 5 cm is

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate of at which kinetic energy is imparted to water?

A man weighing 60 kg climbs a staircase carrying a 20 kg load on his hand.The staircase has 20 steps and each steps has height of 20 cm.If he takes 20s to climb, his power is

A particle A suffers on oblique elastic collision with a particle B that is at rest initially.If their masses are the same, then after the collision
1. Their KE may be equal
2. A continues to move in the original direction while B remains constant
3. They will move in mutually perpendicular directions
4. A comes to rest and B starts moving in the direction of the original motion of A

Two particles of masses m₁ m₂ move with initial velocities u₁ and u₂ .On collision, one of the particle s get excited to higher level, after absorbing energy E.If final velocities of particles be v₁ and v₂, then we must have

A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 ft tall building. After a fall of 30 ft each towards the earth,their respective kinetic energies will be in the ratio of

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio of

Two similar springs P and Q have spring constants kᴘ and kǫ, such that kᴘ > kǫ. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs Wᴘ and Wǫ are related as, in case (a) and case(b), respectively

A ballon with mass m is descending with an acceleration a(where, a

A uniform force of (3i+j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2i+k)m to position (4i+3j-k)m. The work done by the force on the particle is

An explosions breaks rock into three parts in a horizontal plane.Two of them go off at right angles top each other.The first part of mass 1 kg moves with a speed of 12 ms⁻¹ and the second part of mass 2 kg moves with 8 ms⁻¹ speed.If the third part flies off with 4 ms⁻¹ speed, then its mass is

For inelastic collision between two spherical rigid bodies

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 ms⁻¹ and 2 kg second part moving with a velocity of 8 ms⁻¹. If the third part flies off with a velocity of 4 ms⁻¹, its mass would be:

A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5s. Each bullet has a mass of 10 g with a muzzle velocity of 800 ms⁻¹. The final velocity acquired by the person and the average force exerted on the person are

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 ms⁻¹. It collides with a horizontal spring of force constant 200 Nm⁻¹. The maximum compression produced in the spring will be:

The upper half of an inclined plane of inclination θ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by

A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to mass of 3m velocity 2v. The final velocity of the combination is

Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction

A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:

Water falls from a height of 60m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of energy. How much power is generated by the turbine? ( g = 10 m/s²)

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P₀. The instantaneouos velocity of of this car is proportional to:

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ if energy. This initial velocity of the shell is:

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms⁻¹ and the second part of mass 2 kg moves with speed 8 ms⁻¹. If the third part flies off with speed 4 ms⁻¹ then its mass is

A bullet is shot from a rifle.As a result the rifle recoils.The kinetic energy of rifile as compared to that of bullet is

A circular disc rolls down an inclined plane.The ratio of rotational kinetic energy to total kinetic energy is

A force acts on a 3.0 g particle in such a way that the position of the particle as a function of time is given by x = 3t – 4t² + t³ , where x is in metre and t is in second. The work done during the first 4 s is

Two bodies of masses m₁ and m₂ and having velocities v₁ and v₂ respectively, moving along a straight line are brought to rest by equal resistance forces. If one moves twice as that of the duration of other but goes only 1/2 of the distances covered by the other before coming to rest, the ratio v₁/v₂ and m₁/m₂ are

The kinetic energy of particle moving along a circle of radius R depends upon the distance s as k= as².Then the force acting on particle is

A long horizontal rod has a bead which can slide long its length and initially placed at a distance L from one end A of the rod.The rod is set in angular motion about A with constant angular acceleration α.If the coefficient of friction between the rod and the bead is ? and gravity is neglected, then the time after which the bead starts slipping is

If the angular momentum of any rotating body increase by 200%, then the increase in its kinetic energy

A particle moves from position r₁ = 3i + 2j – 6k to position r₂ = 14i + 13j + 9k under the action of force (4i + j + 3k)N. The work done will be