Power, Force and Velocity

Q. An electric lift with a maximum load of $2000kg$ (lift + passengers) is moving up with a constant speed of $1.5{ms}^{-1}$. The frictional force opposing the motion is $3000N$. The minimum power delivered by the motor to the lift in watts is: $(g=10{ms}^{-2})$

1. $34500$
2. $23000$
3. $20000$
4. $23500$

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

1. $(2t^3+3t^4)\text{W}$
2. $(2t^3+3t^5)\text{W}$
3. $(2t^3+3t^3)\text{W}$
4. $(2t^2+4t^4)\text{W}$

Q. A particle $A$ of mass $\frac{10}{7}\text{kg}$ is moving in the positive $x-$ direction. Its initial position is $x=0$ and initial velocity is $1\text{m/s}$. The velocity at $x=10\text{m}$ in $\text{m/s}$ (use the graph given). Answer the nearest integer.

Q. A $60HP$ electric motor lifts an elevator with a maximum total load capacity of $2000kg$. If the frictional force on the elevator is $4000N$, the speed of the elevator at full load is close to (Given $1HP=746W$, $g=10m/s^2$)

1. $1.5m/s$
2. $2.0m/s$
3. $1.7m/s$
4. $1.9m/s$

Q.

What is a derivative in physics?

Q.

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to

1. t^1/2

2. t

3. t^3/2

4. t²

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. 
2. 
3. 
4. 

Q.

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

1. $t$

2. $t^{3/2}$

3. $t^{1/2}$

4. $t^{2/3}$

Q.

An electric motor exerts a force of 40 N on a cable and pulls it by a distance of 30 m in one minute. The power supplied by the motor (in Watts) is

1. 20

2. 200

3. 2

4. 10

Q. An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is

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. 10 kw
3. 1 kw
4. 100 w

Q. The range R of projectile is same when its maximum heights are $h_1$ and $h_2$. What is the relation between R and $h_1$ and $h_2$

1. 
2. 
3. 
4. 

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

Q.

An electric motor creates a tension of 4500 newton in a hoisting cable and reels it in at the rate of 2 m/sec. What is the power of electric motor

1. 15 kW

2. 9 kW

3. 225 W

4. 9000 HP

Q. A man is riding on a cycle with velocity 7.2 km/hr up a hill having a slope 1 in 20. The total mass of the man and cycle is 100 kg. The power of the man is

1. 125 W
2. 200 W
3. 175 W
4. 98 W

Q. A body of mass $m$ is projected from ground with speed $u$ at an angle $\theta$ with horizontal. The power delivered by gravity when it is at half of maximum height from ground is

1. $\frac{mgu\cos \theta }{\sqrt{2}}$
2. $-\frac{mgu\sin \theta }{\sqrt{2}}$
3. $\frac{mgu\sin \theta }{\sqrt{2}}$
4. Both (b) and (c)

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. 549 W
2. 249 W
3. 100 W
4. 149 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. $\frac{m}{3P}(v_2^2-v_1^2)$
4. $\frac{m}{3P}(v_2^3-v_1^3)$

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. Zero
4. 76.9 kW

Q. A one kilowatt motor pumps out water from a $\text{10 m}$ deep well. Calculate the quantity of water pumped out per second.(Take $g=10\text{m}/{\text{s}}^2$)

1. $\text{10 kg}$
2. $\text{8.96 kg}$
3. $\text{14.3 kg}$
4. $\text{9.8 kg}$

Q. A $50\text{kg}$ 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. $980\text{W}$
2. $245\text{W}$
3. $490\sqrt{3}\text{W}$
4. $490\text{W}$

Q. In the figure shown $P_1$ and $P_2$ are massless pulleys. $P_1$ is fixed and $P_2$ can move. Masses of A, B and C are $\frac{9m}{64},$ $2m$ and $m$ respectively. All contacts are smooth and the string is massless. If $\theta ={\tan }^{-1}\left(\frac{3}{4}\right)$, then the acceleration of block $C$ in $m/s^2$ is

Q.

A dam is situated at a height of 550 metres above sea level and supplies water to a power house which is at a height of 50 metres above sea level. 2000 kg of water passes through the turbines per second. The maximum electrical power output of the power house if the whole system were $80\%$ efficient is

1. 8 MW

2. 10 MW

3. 12.5 MW

4. 16 MW

Q. When a belt moves horizontally at a constant speed of $1.5{\text{ms}}^{-1},$ gravels are falling on it at rate of $5$ ${\text{kg s}}^{-1}.$ Then, the extra power required to drive the belt is

1. $11.25\text{W}$
2. $37.5\text{W}$
3. $7.5\text{W}$
4. $0.75\text{W}$

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

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.

A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to

1. 

2. 

3. 

4. 

Q.

An electric motor creates a tension of $4500N$ in a hoisting cable and reels it in at the rate of $2m/s$. What is the power of the electric motor-

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. 

Q. A stone is projected at time t = 0 with a speed $v_0$ and an angle $\theta$ with the horizontal in a uniform gravitational field. The rate of work done (P) by the gravitational force plotted against time (t) will be as

1. 
2. 
3. 
4.