Power

The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s is: $\left(g = 9.8\text{ m/s}^2\right)$

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to

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

A body of mass 2 kg begins to move under the influence of time dependent force $\vec{F} = \left(2t\hat{i} + 6t^2\hat{j}\right)\text{ N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and y -axis respectively. The power produced by the force at $t = 2\text{ s}$ is ______ W.

If the force acting on a body is inversely proportional to its speed, the kinetic energy of the body is

A constant force $\vec{F} = 3\hat{i} - 2\hat{j} - \hat{k}$ newton has a displacement $\vec{r} = 2\hat{i} - 3\hat{j} - 3\hat{k}$ metre in 2 second. The work done and the power are respectively

A body of mass 4 kg is placed on a plane at a point $P$ having coordinates $(3, 4)\text{ m}$. Under the action of force$\vec{F} = (2\hat{i} + 3\hat{j})\text{ N}$, it moves to a new point Q having coordinates $(6, 10)\text{ m}$ in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of:

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

An object of mass 1000 g experiences a time dependent force $\vec{F} = \left(2t\hat{i} + 3t^2\hat{j}\right)N$. The power generated by the force at time $t$ is:

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., $\frac{dm}{dt} \propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

A body of mass 1 kg starts from rest and moves with uniform acceleration. In 2 seconds, its velocity is $10\text{ m/s}$. The power exerted on the body in one second is

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

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to:

The power $(P)$ is supplied to a rotating body having moment of inertia ' I ' and angular acceleration ' $\alpha$ '. Its instantaneous angular velocity ' $\omega$ ' is

A body of mass $2\text{ kg}$ begins to move under the action of a time dependent force given by $\vec{F} = \left(6t\hat{i} + 6t^2\hat{j}\right)N$. The power developed by the force at the time $t$ is given by:

A particle moves with a velocity $(5\hat{i} - 3\hat{j} + 6\hat{k})\text{ m s}^{-1}$ horizontally under the action of constant force $(10\hat{i} + 10\hat{j} + 20\hat{k})\text{ N}$. The instantaneous power supplied to the particle is:

The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x} + 1}$, that are capable of raising $300\text{ kg}$ water in 5 minutes and $50\text{ kg}$ water in 2 minutes respectively from a well of $100\text{ m}$ deep. The value of $x$ will be

A block of mass $5\text{ kg}$ starting from rest is pulled up on a smooth inclined plane making an angle of $30^\circ$ with horizontal with an effective acceleration of $1\text{ m s}^{-2}$. The power delivered by the pulling force at $t = 10\text{ s}$ from the start is ___________ W.

[use $g = 10\text{ m s}^{-2}$ ]

(calculate the nearest integer value)

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

If the maximum load carried by an elevator is $1400\text{ kg}$ ( $600\text{ kg}$ - Passengers + 800 $\text{kg}$ - elevator), which is moving up with a uniform speed of $3\text{ m s}^{-1}$ and the frictional force acting on it is $2000\text{ N}$, then the maximum power used by the motor is __________ $\text{kW}\ \left(g = 10\text{ m/s}^2\right)$

A body of mass $2\text{ kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in $4\text{ s}$ is $\frac{1}{3}\alpha^2\sqrt{P}\text{ m}$. The value of $\alpha$ will be ______.

The energy that will be ideally radiated by a 100 kW transmitter in 1 hour 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${}^{-2}$)

Sand is being dropped from a stationary dropper at a rate of $0.5\text{ kg s}^{-1}$ on a conveyor belt moving with a velocity of $5\text{ m s}^{-1}$. The power needed to keep the belt moving with the same velocity will be:

Water falls from a height of 60m 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 body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to:

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-

A car of mass '$m$' moving with velocity '$u$' on a straight road in a straight line, doubles its velocity in time t. The power delivered by the engine of a car for doubling the velocity is

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale):

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s2) must be at least:

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to: (1 HP = 746 W, g = 10 ms-2)

A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) _______.

A body of mass 1 kg begins to move under the action of a 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 be developed by the force at the time t?

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of 10 ms−1, the car needs power P. If it needs power $\frac{P}{2}$ while moving downhill at speed v then value of $v$ is:

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 $\times$ 103 kg/m3 and g = 10 m/s2 then the power (in watt) is

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $v$, the electrical power output will be most likely proportional to

A 70 kg man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force F to raise himself. The center of gravity rises by 0.5 m before he leaps. After the leap the c.g. rises by another 1 m. The maximum power delivered by the muscles is: (Take g = 10 ms$-2$)

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 body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

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 through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?

An engine pumps water continuously through a hose. Water leaves the hose with a 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?

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)

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T.$ The instantaneous power delivered to the body as a function of time is given by

A body of mass $\text{'}m\text{'},$ accelerates uniformly from rest to $\text{'}v_1\text{'}$ in time $T$. The instantaneous power delivered to the body as a function of time is given by

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $\text{'}t\text{'}$ is proportional to

If $\vec{F} = \left(60\hat{i} + 15\hat{j} - 3\hat{k}\right)$ N and$\vec{v} = \left(2\hat{i} - 4\hat{j} + 5\hat{k}\right)$ m/s, then instantaneous power is

How much water a pump of $2\text{ kW}$ can raise in one minute to a height of $10\text{ m}$? (take $g = 10\text{ m/s}^2$)