Work, Energy And Power

A bullet of mass 10 g moving horizontally with a velocity of 400 m/s strikes a wooden block of mass 2 kg suspended by a light inextensible string of length 5 m. As a result the centre of gravity of the block rises a vertical distance of 10 cm. The speed of the bullet after it emerges horizontally from the block is

A body of mass 1 kg begins to move under the action of a time-dependent force F=(2t î+3t² ĵ) N, where î and ĵ are unit vectors along the x and y axes. What power will be developed by the force at time t?

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

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 will respectively be

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. The magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8×10⁻⁴ J by the end of the second revolution after the beginning of the motion, is

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

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/s². The work done by the (i) gravitational force and the (ii) resistive force of air is

A body initially at rest, sliding along a frictionless track from a height h, just completes a vertical circle of diameter AB=D. The height h is equal to

A moving block of mass m collides with another stationary block of mass 4m. The lighter block comes to rest after the collision. When the initial velocity of the lighter block is v, the value of the coefficient of restitution (e) is

A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular directions with speed v each. The energy released during the process is

When an object is shot up a long smooth inclined plane kept at 60^° with the horizontal, it travels a distance x₁ along the plane. When the inclination is decreased to 30^° and the same object is shot with the same velocity, it travels a distance x₂. Then x₁:x₂ will be

An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with X as shown in the graph. The velocities of the object at the points X = 8 m and X = 12 m would be, respectively (nearly)

A force F=20+10y acts on a particle in the y-direction, where F is in newton and y in metre. The work done by this force to move the particle from y=0 to y=1 m is

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

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/s²)

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 the Earth and the speed of the particle at that instant are respectively

An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 m/s. The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift (in watts) is (g=10 m/s²)

A particle moves with a velocity (6î-4ĵ+3k̂) m/s under the action of a constant force F=(10î+10ĵ+20k̂) N. The instantaneous power applied to the particle is

A bullet of mass m hits a block of mass M elastically. The transfer of energy is maximum when

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

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

At any instant of time t, the displacement of a particle is given by x=2t-1 (SI units), under the influence of a force of 5 N. The value of the instantaneous power is (in SI units)

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If F_A and F_B are the braking forces 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 v₀ at the lowest point. If the string goes slack at some point P making an angle θ from the horizontal, the ratio of the speed v of the bob at P to its initial speed v₀ is

A particle of mass $M$ moves along a horizontal $x$-axis from $x=0$ to $x=L$. The coefficient of kinetic friction varies as $\mu_k(x)=\mu_0-\alpha x$, where $\mu_0,\alpha$ are constants of appropriate dimensions, so that $\mu_k(L)=0$. The total work done by the frictional force during the motion is $n\mu_0 MgL$. The value of $n$ is:

A bob $B$ of mass $m$ hangs at rest vertically from the ceiling by a massless string of length $10\,$m. A point mass $A$ of mass $m$ travelling horizontally with speed $10\,\text{ms}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ metre after the collision. Taking $g=10\,\text{ms}^{-2}$ and neglecting the size of the bob, the value of $h$ is:

The sum of the kinetic energy and potential energy of a simple pendulum bob is 0.02 J. The speed of the bob at the equilibrium position is approximately (mass of the bob = 20 g)

The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s, is (g=9.8 m/s²)