The restoring force of a spring with a block attached to the free end of the spring is represented by

An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 ms$$-$$1. The frictional force opposing ...

A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The he...

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 the input energy. How much...

A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to...

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial...

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter ...

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m s$$-$$1. Take 'g' constant with a...

Two identical balls A and B having velocities of 0.5 m s$$-$$1 and $$-$$0.3 m s$$-$$1 respectively collide elastically in one dimension. The velocit...

A bullet of mass 10 g moving horizontally with a velocity of 400 m s$$-$$1 strikes a wood block of mass 2 kg which is suspended by light inextensible ...

A particle moves from a point $$\left( { - 2\widehat i + 5\widehat j} \right)$$ to $$\left( {4\widehat j + 3\widehat k} \right)$$ when a force of $$\l...

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if t...

A body of mass 1 kg begins to move under the action of a time dependent force $$\overrightarrow F = \left( {2t\widehat i + 3{t^2}\widehat J} \right)N...

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

Two particles A and B, move with constant velocities $$\overrightarrow {{v_1}} $$ and $$\overrightarrow {{v_2}} $$. At the initial moment their positi...

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, losses 50 percent of its energy ...

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 $$ \...

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. Afte...

A block of mass 10 kg, moving in x direction with a constant speed of 10 m s$$-$$1, is subjected to a retarding force F = 0.1x J/m during its travel f...

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...

Two particles of masses m1, m2 move with initial velocities u1 and u2. On collision, one of the particles get excited to higher level, after absorbin...

Two similar springs P and Q have spring constants KP and KQ, such that KP > KQ. They are stretched first by the same amount (case a), then by the s...

A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each oth...

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

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. ...

A uniform force of $$\left( {3\widehat i + \widehat j} \right)$$ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position...

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 instantaneous v...

The potential energy of a particle in a force field is $$U = {A \over {{r^2}}} - {B \over r}$$ where A and B are positive constants and r is the dista...

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 h...

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s$$-$$1. It collides with a horizontal spring of force constant 200...

A mass m moving horizontally (along the x-axis) with velocity $$v$$ collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) w...

The potential energy of a system increases if work is done

Force F on a particle moving in a straight line varies with distance d as shown in figure. The work done on the particle during its displacement of ...

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 gravitatio...

A particle of mass m is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small,...

A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is...

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 the...

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 ...

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 d...

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 1...

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is rel...

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...

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power i...

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

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on...

300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Work done against friction is (Take g = 10 m/s2)

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = $${1 \over 3}$$t2, where t is i...

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 m s$$-$$1. The kinetic energy of the ...

A force F acting on an object varies with distance x as shown here. The force is in N and x in m. The work done by the force in moving the object fr...

A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet ball building. After a fall of 30 feet each towards earth, their resp...

A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2. Both of them have the same momentum...

A mass of 0.5 kg moving with a speed of 1.5 m/s on horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. T...

When a long spring is stretched by 2 cm, its potential energy is U. If the spring is stretched by 10 cm, the potential energy stored in it will be

A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their ...

If kinetic energy of a body is increased by 300% then percentage change in momentum will be

A child is sitting on a swing. Its minimum and maximum heights from the ground 0.75 m and 2 m respectively, its maximum speed will be

A particle is projected making an angle of 45o with horizontal having kinetic energy K. The kinetic energy at highest point will be

Two springs A and B having spring constant KA and KB (KA = 2KB) are stretched by applying force of equal magnitude. If energy stored in spring A is EA...

If $$\overrightarrow F = \left( {60\widehat i + 15\widehat j - 3\widehat k} \right)$$ N and $$\overrightarrow v = \left( {2\widehat i - 4\widehat j ...

A mass of 1 kg is thrown up with a velocity of 100 m/s. After 5 seconds, it explodes into two parts. One part of mass 400 g comes down with a velocity...