Work, Energy and Power PYQs

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)

The kinetic energies of two similar cars A and B are $100\,\text{J}$ and $225\,\text{J}$ respectively. On applying brakes, car A stops after $1000\,\text{m}$ and car B stops after $1500\,\text{m}$. If $F_A$ and $F_B$ are the forces applied by the brakes on cars A and B respectively, then the ratio $\dfrac{F_A}{F_B}$ is

A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity v₀ as shown in figure. If the string gets slack at some point P making an angle θ from the horizontal, the ratio of the speed v of the bob at point P to its initial speed v₀ is:

A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take g = 9.8 m/s²)

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

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)

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)

An object of mass $500\ \text{g}$, initially at rest, is acted upon by a variable force whose $x$-component varies with $x$ in the manner shown. The velocities of the object at the points $x = 8\ \text{m}$ and $x = 12\ \text{m}$ would have the respective values of (nearly):

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:

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, the value of coefficient of restitution (e) will be:

Consider a drop of rain water having mass $1\,\text{g}$ falling from a height of $1\,\text{km}$. It hits the ground with a speed of $50\,\text{m/s}$. Take $g$ constant with a value $10\,\text{m/s}^2$. The work done by (i) gravitational force and (ii) resistive force of air is:

A bullet of mass $10\ \text{g}$ moving horizontally with a velocity of $400\ \text{m s}^{-1}$ strikes a wood block of mass $2\ \text{kg}$ suspended by a light inextensible string of length $5\ \text{m}$. As a result, the centre of gravity of the block rises through a vertical distance of $10\ \text{cm}$. The speed of the bullet after it emerges horizontally from the block will be:

A particle moves from a point $(-2\hat{i}+5\hat{j})$ to $(4\hat{j}+3\hat{k})$ when a force $(4\hat{i}+3\hat{j})\ \text{N}$ is applied. How much work has been done by the force?

A ball is thrown vertically downwards from a height of $20\,\text{m}$ with an initial velocity $v_0$. It collides with the ground, loses $50\%$ of its energy in collision and rebounds to the same height. The initial velocity $v_0$ is: (Take $g=10\,\text{ms}^{-2}$)

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is:

A uniform force of $(3\hat{i}+\hat{j})$ newton acts on a particle of mass $2\,\mathrm{kg}$. Hence the particle is displaced from position $(2\hat{i}+\hat{k})$ metre to position $(4\hat{i}+3\hat{j}-\hat{k})$ metre. The work done by the force on the particle is:

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P₀. The instantaneous velocity of this car is proportional to:

A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is:

An engine pumps water continuously through a hose. Water leaves the hose with velocity $v$ 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 $1\,\mathrm{kg}$ is thrown vertically upward with velocity $20\,\mathrm{m/s}$. It momentarily comes to rest after reaching a height of $18\,\mathrm{m}$. How much energy is lost due to air friction? ($g=10\,\mathrm{m/s^2}$)

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? (g = 10 m/s²)

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

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 bomb of mass $30\,kg$ at rest explodes into two pieces of masses $18\,kg$ and $12\,kg$. The velocity of $18\,kg$ mass is $6\,m\,s^{-1}$. The kinetic energy of the other mass is:

A force F acting on an object varies with distance x as shown here. The force is in N and x is in m. The work done by the force in moving the object from x = 0 to x = 6 m is :