A body of mass 1 kg begins to move under the action of a time dependent force F =(2t Î +3t²ĵ) N, where î and ĵ are unit vectors along x and y axes. What power will be developed by the force at the time (t) ?

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?

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 the kinetic enegry of the particle becomes equal to 8 × 10^-4 J by the end of the second revolution after the beginning of the motion ?

Two identical balls A and B having velocities of 0.5 m/s and 0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be

A particle moves from a point (-2Î +5ĵ) to (4ĵ +3ķ) when a force of (4Î +3ĵ) N is applied. How much work has been done by the force ?

Two similar springs P and Q have spring constants K_p and K_Q , such that K_p > K_Q .They are stretched, first by the same amount (case α), then by the same force (case b). The work done by the springs W_p and W_Q are related as, in case (α) and case (b),respectively

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

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

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

A mass m moves in a circle on a smooth horizontal plane with velocity ν₀ at a radius R₀ . The mass is attached to a string which passes through a smooth hole in the plane as shown.

The tension in the string is increased gradually and finally m moves in a circle of radius R₀/2 . The final value of the kinetic energy is

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v₀ . It collides with the ground, loses 50% of its energy in collision and rebounds to the same height.The initial velocity v₀ is (Take, g = 1 ms^-2)

The heart of a man 5 L of blood through the arteries per minute at a pressure of 150 mm of mercury.If the density of mercury be 13.6 × 10³ kg/m³ and g = 10 m/s² , then the power of heart in watt is

On a friction less surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle θ to its initial direction and has a speed v/3. The second block's speed after the collision is

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 uniform force of (3Î + ĵ ) N acts on a particle of mass 2 kg. Hence, the particle is displaced from position (2Î +ĵ ) m to position (4Î + 3ĵ -ķ) m. The work done by the force on the particle is

A body of mass m taken from the earths's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

The potential energy of a particle in a force field is U = A/r² -B/r, where A and B are positive constants and r is the distance of particle from the center of the field. For stable equilibrium, the distance of the particle is

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 the figure. The work done on the particle during its displacement of 12 m is

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 ms^-1. The mass per unit length of water in the pipe is 100 kg m^-1. What is the power of the engine?

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produce in the length of the spring will be

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

A body of mass 1 kg is thrown upwards with a velocity

20 ms^-1 . The momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friciton? (Take g = 10 ms^-2 )

An explosion blows a rock into three parts. Three 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 shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generation 1.05 kJ of energy. The initial velocity of the shell 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 is generated by the turbine ?

( Takeg = 10 m/s² )

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

A body of mass 3 klg is under a constant force, which causes a displacement s in meter in it, given by the relation

s = 1/2 × t²

where t is in second. work done by the force in 2 s is

A force F acting on an object varies with distance x as shown here. The forces is in newton and x is in meter. The work done by the force in moving the object from

x = 0 to x = 6 m is

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The kinetic energy of the other mass is

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The kinetic energy of the other mass is

A particle of mass m₁ is moving with a velocity ν₁ and another particle of a mass m₂ is moving with a velocity ν₂ . Both of them have the same momentum, but their different kinetic energies are E₁ and E₂ respectively. If m₁ > m₂

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

A stone is tied to a string of length Ι and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is as its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is hortizontal (g being acceleration due to gravity) is

A stationary particle explodes into two particles of a masses m₁ and m₂, which move in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁ / E₂ is

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

A stone is thrown at an angle of 45° to the horizontal with kinetic energy Ķ. The kinetic energy at the highest point is

A child is swinging a swing. Minimum and maximum heights of swing from the earth's surface are 0.75 m and 2 m respectively. The maximum velocity of this swing is

Two bodies with kinetic energies in the ratio 4 : 1 are moving with equal linear momentum. The ratio of their masses is

Two equal masses m₁ and m₂ moving along the same straight line with velocities +3 m/s and -5 m/s respectively collide elastically. Their velocities after the collision will be respectively

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 = 3 t - 4t² +t ³, where x is in meter and t in second. The work done during the first 4 s is

A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together the loss in kinetic energy due to collision is

A body of mass m moving with velocity 3 km/h collides with a body of mass 2 m at rest. Now, the coalesced mass starts to move with a velocity

If the momentum of a body is increased by 50%, then the percentage increase in its kinetic energy is

The KE acquired by a mass m is travelling a certain distance d, starting from rest under the action of a constant force is directly proportional to

Two masses 1 g and 9 g are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is

A position dependent force

F =(7 -2x +3x² ) N, acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m. Work done in joule is

Two identical balls A and B moving with velocities + 0.5 m/s and -0.3 m/s respectively, collide head on elastically. The velocity of the balls A and B after collision will be repectively

How much a water a pump of 2 kW can raise in one minute to a height of 10 m

(Take g = 10 m/s² )

A bullet of mass 10 g leaves a rifle at an initial velocity of 1000 m/s and strikes the earth at the same level with a velocity of 500 m/s. The work done in joule to overcome the resistance of air will be

The coefficient of restitution e for a perfectly elastic collision is