Work, Energy an...

The work done in pulling up a block of wood weighing 2 kN for a length of 10 m on a smooth plane inclined at an angle of 15° with the horizontal is ________. (sin 15° = 0.2588)

The scalar product of vectors is

A crane is used to lift 10000 kg of coal from a mine 100 m deep. If the time taken to lift coal by the crane is 1 hour, then what is the power of the driving mechanism of the crane?
(Efficiency of the crane is 80%, g = 9.8 m/s²)

The scalar product of two vectors A and B in terms of the magnitudes and angle θ is

Two carts on horizontal straight rails are pushed apart by an explosion of a powder charge Q placed between the carts. Let the coefficient of friction () between the two carts and rails be identical. If the 400 kg cart travels a distance of 46 m and stops, the distance covered by the cart weighing 800 kg is 

The scalar product of two vectors A and B is

The figure above shows a smooth curved track terminating in a smooth horizontal part. A spring of spring constant 400 N/m is attached at one end to the wedge fixed rigidly with the horizontal part. A 40 g mass is released from a position of rest at a height of 4.9 m on the curved track. What is the maximum compression of the spring? (Take g = 9.8 m/s²)

A 1 kg ball moving at 12 m/s collides head-on with a 2 kg ball moving in the opposite direction at 24 m/s. What is the velocity of each ball after the impact if the coefficient of restitution is ?

If a bag of mass M hangs by a long thread and a bullet of mass m comes horizontally with velocity v and gets caught in the bag, then for combined (bag + bullet) system

A body of mass 400 g is rotating in a circular path of radius r with constant velocity. What is the work done in one complete revolution?

The PE between 2 atoms in a molecule is given by u(x) =  where a and b are positive constants and x is the distance between the atoms. The atoms are in stable equilibrium when ________.

A pendulum consists of a wooden bob of mass m and length l. A bullet of mass m₁ is fired towards the pendulum with a speed v₁. If the bullet emerges out of the bob with a speed , and the bob just completes motion along a vertical circle, then v₁ is

A particle of mass m has half the kinetic energy of another particle of mass m/2. If the speed of the heavier particle is increased by 2 ms^–1, its new kinetic energy equals the original kinetic energy of the lighter particle. The ratio of the original speeds of the lighter and heavier particles is

If the speed of a vehicle increases by 3 m/s, its KE is doubled. The original speed of the vehicle was

A body falling from a height of 10 m rebounds from a hard floor. If it loses 20% of its energy during the impact, then it will rise up to

If the momentum of a body is increased by 60%, then its KE increases by

A solid ball of density half that of water falls freely under gravity from a height of 18.6 m and then enters water. Up to what depth will the ball go? (g = 9.8 m/s²)

A particle moves under the effect of a force F = cx from x = 0 to x₁. The work done in the process is 

The scalar product of two vectors A and B in terms of the projections of the vectors on the x, y and z axis is

A uniform chain of length L and mass M is lying on a smooth table and  of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on the table is

The change in kinetic energy of a particle is equal to the

A bullet of mass m moving with a horizontal velocity v₁ strikes a stationary block of mass M suspended by a string of length L. The bullet gets embedded in the block. What is the maximum angle made by the string after the impact?

What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to a vertical height of 20 cm? (g = 9.8 m/s²)

A shell is fired from a canon with velocity v m/s at an angle  with the horizontal direction. At the highest point in its path it explodes into pieces of equal mass. One of the pieces retraces its path to the canon and the speed in m/s of the other piece immediately after the explosion is _________.

A cord is used to lower vertically a block of mass m to a distance d at a constant downward acceleration of . The work done by the cord on the block is