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

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 the motion is 3000 N . The minimum power delivered by the motor to the lift in watts is : (g = 10 ms⁻²)

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 AB = D.The height h is equal to

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

A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity \(v_0\) as shown in the figure. If the string gets slack at some point P making an angle \(\theta\) from the horizontal, the ratio of the speed v of the bob at point P to its initial speed \(v_0\) is:

The kinetic energies of two similar cars A and B are 100J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m. If \(\text{F}_\text{A}\) and \(\text{F}_\text{B}\) are the forces applied by the breaks on cars A and B, respectively, then the ratio \(\text{F}_\text{A}\,/ \,\text{F}_\text{B}\) is

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v₁ while body B is at rest before collision. The velocity of the system after collision is v₂. The ratio v₁ : v₂ is

A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm.The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes:

At any instant of time t, the displacement of any particle is given by 2t −1 (SI unit) under the influence of force of 5N. The value of instantaneous power is (in SI unit):

The energy that will be ideally radiated by a 100kW transmitter in 1 hour is

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

Body A of mass 4 m moving with speed u collides with another body B of mass 2 m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is

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 y = 1m is

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

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 velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

Consider a drop of rain water having mass 1 g falling from a height of 1km. It hits the ground with a speed of 50ms⁻¹. Take 'g' constant with a value 10ms⁻².The work done by the (i) gravitational force and the (ii) resistive force of air is

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 energy of the particle becomes equal to 8 × 10⁻⁴J by the end of the second revolution after the beginning of the motion ?

A body of mass 1 kg begins to move under the action of time dependent force \(\vec{F}\) = \(\left(2t\hat{i} + 3t^2\hat{j}\right)\) N , where \(\hat{i}\) and \(\hat{j}\) are unit vectors along x and y axis.What power will developed by the force at the time (t) ?