Power, Force and Velocity

Q. A force $(4\hat{i}+\hat{j}-2\hat{k})\text{N}$ acting on a body maintains its velocity at $(2\hat{i}+3\hat{j}-\hat{k})\text{m/s}$. The power exerted is

1. $15\text{W}$
2. $13\text{W}$
3. $12\text{W}$
4. $20\text{W}$

Q. A ball of mass $5\text{kg}$ is dropped from a tower. Find the power of gravitational force at time $t=2\text{seconds}$.
(Take $g=10{\text{m/s}}^2$)

1. $1000\text{W}$
2. $2000\text{W}$
3. $100\text{W}$
4. $200\text{W}$

Q. A particle of mass $m$ starts moving in a circular path $A$ of constant radius $r$ in such a way that its centripetal acceleration $a_c$ is changing with time as $a_c=k^2{r}^2{t}^2$ where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

1. $m{k}^2{r}^4{t}^2$
2. $m{k}^2{r}^2{t}^2$
3. $m{k}^2{r}^{3}t$
4. $mk{r}^4{t}^2$

Q.

In the streamlined flow of a liquid, the power due to the pressure difference between the ends of the tube is

1. Equal to a product of pressure and volume of liquid flowing per second.

2. Equal to a product of pressure and mass of liquid flowing per second.

3. Equal to the product of radius and coefficient of viscosity.

4. Equal to the product of pressure and velocity.

Q. A boy whose mass is $30\text{kg}$ climbs with a constant speed on a vertical rope of $6\text{m}$ length in $10\text{s}$. The power of the boy during the climb is
(Take $g=10{\text{m/s}}^2)$

1. $60\text{W}$
2. $3000\text{W}$
3. $180\text{W}$
4. $5\text{W}$

Q. A particle of mass $0.2\text{kg}$ (initially at rest) starts moving in one dimension under a force that delivers a constant power $0.5W$ to the particle. Then the speed after $5\text{seconds}$ is

1. $20\text{m/s}$
2. $5\text{m/s}$
3. $10\text{m/s}$
4. $20\text{m/s}$

Q. A body of mass $5\text{kg}$ starts from rest and moves in a straight line under the influence of two variable forces $F_1=(10t+\frac{6}{t})\text{N}$ and $F_2=(15-\frac{6}{t})\text{N}$, acting in same direction. Find the power delivered by force $F_1$ at $t=2\text{sec}$.

1. $130\text{J/s}$
2. $230\text{J/s}$
3. $30\text{J/s}$
4. $350\text{J/s}$

Q. A car of 100 HP is moving with a constant velocity of 72 km/hour. The forward force exerted by the engine of the car is

1. $3.73\times {10}^{3}N$
2. $3.72\times {10}^{2}N$
3. $3.73\times {10}^{1}N$
4. $Noneoftheabove$

Q. Figure shows an ideal spring block system, force constant of spring is k which has been compressed by an amount $x_0$. If $x$ is instantaneous deflection of spring from its natural length, mark the correct option (s).

1. Instantaneous power developed by spring is $P=kx\sqrt{\frac{k}{m}(x_0^2-x^2)}$
2. Maximum power of spring is $\frac{k}{2}\sqrt{\frac{k}{m}}{x}_0^2$
3. Maximum power occurs at $x=\frac{x_0}{\sqrt{2}}$
4. Maximum power occurs at $x=\frac{x_0}{2}$

Q. In unloading grain from the hold of a ship, an elevator lifts the grain through a height of 12 m. Grain is discharged at the top of the elevator at a rate of 2 kg/s, and the discharge speed of each grain particle is 3m/s. Then, the minimum power of the motor that can elevate grain in this way is

1. 149 W
2. 249 W
3. 100 W
4. 549 W

Q. A particle of mass $0.2\text{kg}$ is moving in one dimension under a force that delivers a constant power $0.5\text{W}$ to the particle. If the initial speed (in $\text{m/s})$ of the particle is zero, then speed in $\left(\text{m/s}\right)$ after $5\text{s}$ is

1. $2.5\text{m/s}$
2. $5\text{m/s}$
3. $10\text{m/s}$
4. $3\text{m/s}$

Q. An electric motor produces a tension of 4500N in a load lifting cable and rolls it at the rate of 2m/s. The power of the motor is

1. 9 kW
2. 15 kW
3. 225 kW
4. $9\times {10}^{3}hp$

Q. An advertisement claims that a certain 1200 kg car can accelerate from rest to a speed of 25 m/s in a time of 8s. What average power must the motor produce to cause this acceleration? (Ignore friction losses)

1. 46.9 kW
2. 56.9 kW
3. 76.9 kW
4. Zero

Q. A mass m falls from rest under the influence of gravity. Then the average power supplied to the mass by the force of gravity is

1. $P=m\sqrt{\frac{g^{3}h}{3}}$
2. $P=m\sqrt{\frac{g^{3}h}{12}}$
3. $P=2m\sqrt{\frac{g^{3}h}{2}}$
4. $P=m\sqrt{\frac{g^{3}h}{2}}$
   where h is the distance the mass falls.

Q. What is the power required by the pump to lift $1000\text{kg}$ of water per minute from a $20\text{m}$ deep well and eject it with the speed of $20\text{m/s}$?

1. $3666.7\text{W}$
2. $4666.7\text{W}$
3. $6666.7\text{W}$
4. $5666.7\text{W}$

Q. Water from a stream is falling on the blades of a turbine at the rate of 100kg/sec. If the height of the stream is 100m then the power delivered to the turbine is

1. 100 kw
2. 100 w
3. 10 kw
4. 1 kw

Q. Power supplied to a particle of mass 2 kg varies with time as $p=\frac{3t^2}{2}$ watt. Here 't' is in second. If velocity of particle at t = 0 is v = 0. The velocity of particle at time t = 2 second will be

1. 1 m/s
2. 4 m/s
3. 2 m/s
4. $2\sqrt{2}m/s$

Q. A body at rest starts moving under the action of a constant force along a straight line. The instantaneous power developed by this force with time $\text{t}$ is correctly represented by

1. 
2. 
3. 
4. 

Q. Water from a stream is falling on the blades of a turbine at the rate of 100kg/sec. If the height of the stream is 100m then the power delivered to the turbine is

1. 100 kw
2. 100 w
3. 10 kw
4. 1 kw

Q. A hoist operated by an electric motor has a mass of 500 kg. It raises a load of 300 kg vertically at a steady speed of 0.2 m/s. Frictional resistance can be taken to be constant at 1200 N. What is the power required?

1. 1.51 kW
2. 1.81 kW
3. 2.01 kW
4. 1.61 kW

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

1. $\sqrt{1}$
2. $t^{3/2}$
3. $t^{3/4}$
4. $t^2$

Q. A force $F$ acting on a body depends on its displacement $x$ as $F\propto x^{\frac{-1}{3}}$. The power delivered by $F$ will depend on displacement as

1. $x^{\frac{2}{3}}$
2. $x^{\frac{5}{3}}$
3. $x^{\frac{1}{2}}$
4. $x^0$

Q. A man is pulling a block resting on the ground by applying force $F=(20t+40)\text{N}$ as shown in the figure. If the pulley is frictionless and mass of the block is $4\text{kg}$, find out the power delivered by the force, $3\text{seconds}$ after the man starts pulling the block. (Take $g=10{\text{m/s}}^2$)

1. $2250\text{J/s}$
2. $5250\text{J/s}$
3. $3000\text{J/s}$
4. $1250\text{J/s}$

Q. A force $(4\hat{i}+\hat{j}-2\hat{k})\text{N}$ acting on a body maintains its velocity at $(2\hat{i}+3\hat{j}-\hat{k})\text{m/s}$. The power exerted is

1. $15\text{W}$
2. $13\text{W}$
3. $12\text{W}$
4. $20\text{W}$

Q. A constant power $P$ is applied to a particle of mass $m$. The distance travelled by the particle when its velocity increases from $v_1\text{to}{v}_2$ is - (neglect friction)

1. $\frac{3P}{m}(v_2^2-v_1^2)$
2. $\frac{m}{3P}(v_2-v_1)$
3. $\frac{m}{3P}(v_2^3-v_1^3)$
4. $\frac{m}{3P}(v_2^2-v_1^2)$

Q. An engine generates a power of $75\text{kW}$ having efficiency of $80\%$ and the car moves with a constant velocity of $20\text{m/s}$. Find the force generated by the engine. (Assume the engine applies a constant force on the car)

1. $2000\text{N}$
2. $3000\text{N}$
3. $6000\text{N}$
4. $1500\text{N}$

Q. A $40\text{kg}$ girl is swinging on a swing from rest. Then, the power delivered when moving with a velocity of $2\text{m/s}$ upwards in a direction making an angle ${60}^{\circ }$ with the vertical is

1. $248\sqrt{3}\text{W}$
2. $392\sqrt{3}\text{W}$
3. $448\text{W}$
4. $580\text{W}$

Q. A block of mass $2\text{kg}$ initially at rest moves under the influence of a time-dependent force $\overrightarrow{F}=4tN\hat{i}.$ The power developed by the force at $t=2\text{second}$ is

1. $16\text{W}$
2. $32\text{W}$
3. $48\text{W}$
4. $30\text{W}$

Q. A particle of mass $m$ starts moving in a circular path $A$ of constant radius $r$ in such a way that its centripetal acceleration $a_c$ is changing with time as $a_c=k^2{r}^2{t}^2$ where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

1. $m{k}^2{r}^4{t}^2$
2. $m{k}^2{r}^2{t}^2$
3. $m{k}^2{r}^{3}t$
4. $mk{r}^4{t}^2$

Q. Power supplied to a particle of mass $5\text{kg}$ varies with time as $P=\frac{4t^3}{5}\text{W}$, where $t$ is in $\text{seconds}$. If the velocity of the particle at $t=0$ is zero, then what will be the velocity of the particle at $5\text{seconds}$?

1. $5\sqrt{2}\text{m/s}$
2. $\sqrt{2}\text{m/s}$
3. $5\text{m/s}$
4. $2\text{m/s}$