Average and Instaneous Power

Q.

Calculate the power of a pump that can lift $200kg$ of water through a height of $10m$ in $5s$. Given the value of $g=10m{s}^{-2}$.

Q.

The power of a pump, which can pump 200kg of water to a height of 200m in 10sec is ($g=10m/s^{-2}$)

1. 40 kW

2. 80 kW

3. 400 kW

4. 960 kW

Q. A dipole is placed in an electric field as shown. In which direction will it move ?
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1. Towards the right as its potential energy will decrease.
2. Towards the left as its potential energy will increase.
3. Towards the left as its potential energy will decrease.
4. Towards the right as its potential energy will increase.

Q. A block of mass $m=3\text{kg}$ is pulled by a force $F=50\text{N}$ upwards through $2\text{m}$ height in vertical direction. It takes $8\text{seconds}$ to lift the mass. Find the average power delivered by the force.

1. $12.5\text{W}$
2. $25\text{W}$
3. $20\text{W}$
4. $50\text{W}$

Q. The time taken by an engine of power $10\text{kW}$ to lift a mass of $200\text{kg}$ to a height of $40\text{m}$ is $(g=10m{s}^{-2})$

1. $2s$
2. $4s$
3. $8s$
4. $16s$

Q.

Which one of the following is ‘watt’?

1. $kgm{s}^{-2}$

2. $Nm{s}^{-2}$

3. $kg{m}^2{s}^{-3}$

4. $Nm{s}^{-1}$

Q. If the force $\overrightarrow{F}=(60\hat{i}+15\hat{j}-3\hat{k})\text{N}$ and velocity $\overrightarrow{v}=(2\hat{i}-4\hat{j}+5\hat{k})\text{m/s}$, then instantaneous power is

1. $195\text{watt}$
2. $45\text{watt}$
3. $75\text{watt}$
4. $100\text{watt}$

Q. A block of mass $m=3\text{kg}$ is pulled by a force $F=50\text{N}$ upwards through $2\text{m}$ height in vertical direction. It takes $8\text{seconds}$ to lift the mass. Find the average power delivered by the force.

1. $12.5\text{W}$
2. $25\text{W}$
3. $20\text{W}$
4. $50\text{W}$

Q. A pump is required to lift $800\text{kg}$ of water per minute from a $10\text{m}$ deep well and eject it with speed of $20\text{m/s}$. The power required (in watts) of the pump will be
(Take $g=10m/s^2$)

1. $6000$
2. $4000$
3. $5000$
4. $8000$

Q. An engine pumps up $100\text{kg}$ of water through a height of $10\text{m}$ in $5\text{s}$. Given that the efficiency of the engine is $60\%$, what is the power of the engine? (Take $g=10m/s^2$)

1. $33\text{kW}$
2. $3.3\text{kW}$
3. $0.33\text{kW}$
4. $0.033\text{kW}$

Q. A particle of mass $2\text{kg}$ is moving in $xy$ plane under the action of a force. Its velocity and acceleration at a certain instant of time are given by $\overrightarrow{v}=(3\hat{i}+4\hat{j})\text{m/s}$ and $\overrightarrow{a}=(5\hat{i}+4\hat{j}){\text{m/s}}^2$. Find the power delivered by the force at that instant of time.

1. $60\text{W}$
2. $62\text{W}$
3. $64\text{W}$
4. $66\text{W}$

Q. A particle of mass $2\text{kg}$ is moving in $xy$ plane under the action of a force. Its velocity and acceleration at a certain instant of time are given by $\overrightarrow{v}=(3\hat{i}+4\hat{j})\text{m/s}$ and $\overrightarrow{a}=(5\hat{i}+4\hat{j}){\text{m/s}}^2$. Find the power delivered by the force at that instant of time.

1. $60\text{W}$
2. $62\text{W}$
3. $64\text{W}$
4. $66\text{W}$

Q.

A 12 HP motor has to be operated 8 hours/day. How much will it cost at the rate of 50 paisa/kWh in 10 days

1. Rs. 350/-

2. Rs. 358/-

3. Rs. 375/-

4. Rs. 397/-

Q. Water falls from a height of $80\text{m}$ at the rate of $20\text{kg/s}$ to operate a turbine. The losses due to frictional force are $20$ % of the energy. How much power is generated by the turbine? $(g=10\frac{m}{s^2})$

1. $12.3\text{kW}$
2. $7.0\text{kW}$
3. $12.8\text{kW}$
4. $10.2\text{kW}$

Q. A body of mass $1\text{kg}$ begins to move under the action of a time dependent force $\overrightarrow{F}=(2t\hat{i}+3t^2\hat{j})\text{N}$. Calculate the instantaneous power developed at time $t$ ?

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

Q. The time taken by an engine of power $10\text{kW}$ to lift a mass of $200\text{kg}$ to a height of $40\text{m}$ is $(g=10m{s}^{-2})$

1. $2s$
2. $4s$
3. $8s$
4. $16s$

Q. A power $P=2t^3$ is applied to the particle initially at rest. If the kinetic energy of the particle is $K$ and velocity is $v$ then

1. $K\propto t^2$
2. $v\propto t^4$
3. $K\propto t^4$
4. $v\propto t^2$

Q. 7 luggage of mass 10 kg each, fall on a horizontal conveyor belt in an airport moving at 2 m/s in every 5 seconds. Power of motor operating the belt is __.

1. 
   56 watt
2. 
   70 watt
3. 
   112 watt
4. 
   140 watt

Q. 7 luggage of mass 10 kg each, fall on a horizontal conveyor belt in an airport moving at 2 m/s in every 5 seconds. Power of motor operating the belt is __.

1. 
   56 watt
2. 
   70 watt
3. 
   112 watt
4. 
   140 watt

Q.

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

1. $t^{\frac{1}{2}}$

2. $t^{\frac{3}{4}}$

3. $t^{\frac{3}{2}}$

4. $t^2$

Q. A particle of mass m moving in a circular path of constant radius r such that centripetal acceleration $a_c$ is varying with time t as $a_c=krt$ where $k$ is constant, then:

1. Power delivered by the centripetal force is zero
2. Power delivered by the tangential force is $\frac{k{r}^2}{2}$
3. Power delivered by the net force is equal to power delivered by tangential force
4. Tangential force $=\frac{mr}{2}\sqrt{\frac{k}{t}}$

Q. An object of mass $m$, initially at rest under the action of a constant force $F$ attains a velocity $v$ in time $t$. Then, the average power supplied to mass is

1. $\frac{m{v}^2}{2t}$
2. $\frac{Fv}{2}$
3. Both $a$ and $b$ are correct
4. Both $a$ and $b$ are wrong

Q. A particle of mass $m$ is lying on a smooth horizontal surface. A tangential force $F$ is applied to it, then instantaneous power delivered to the particle is

1. $\frac{F^{2}t}{m}$
2. $\frac{F^{2}t}{2m}$
3. $\frac{Ft}{m}$
4. $\frac{Ft}{2m}$

Q.

A truck moving on a smooth horizontal surface with a uniform speed u is carrying stone-dust. If a mass $\Delta m$ of the stone-dust leaks from the truck in a time $\Delta t$, the force needed to keep the truck moving at its uniform speed is

1. $u\frac{\Delta m}{\Delta t}$

2. $\Delta m\frac{du}{dt}$

3. $u\frac{\Delta m}{\Delta t}+\left(\Delta m\right)\frac{du}{dt}$

4. zero