Work, Energy and Power

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

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 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:

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):

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity \(v_1\) while body B is at rest before collision. The velocity of the system after collision is \(v_2\). The ratio \(v_1 : v_2\) is :

The potential energy of a long spring when stretched by 2 cm 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 \(\text{ms}^{-1}\). The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is : (g = 10 \(\text{ms}^{-2}\))

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 height from the surface of earth and the speed of the particle at that instant are respectively :

Water falls from a height of 60 m 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 power is generated by the turbine ? (g = 10 m/s\(^2\))

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

Body A of mass 4m moving with speed \(u\) collides with another body B of mass 2m, 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 \(y = 1\) m is :

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec E\). Due to the force \(q\vec E\), its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

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

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

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. Take 'g' constant with a value 10 m/s\(^2\). The work done by the (i) gravitational force and the (ii) resistive force of air is :

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

A bullet of mass 10 g moving horizontally with a velocity of 400 m s\(^{-1}\) strikes a wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be

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 \((-2\hat i+5\hat j)\) to \((4\hat j+3\hat k)\) when a force of \((4\hat i+3\hat j)\) N is applied. How much work has been done by the force?