Average and Instaneous Power

Q. Convert 1 kilowatt hour into joule.

Q.

What is the relationship between power, force and velocity?

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. 400 kW

2. 960 kW

3. 40 kW

4. 80 kW

Q.

When a constant force is applied to a body moving with a constant acceleration, is power of the force constant? If not, how will force vary with speed for the power to be constant?

Q.

Calculate the power of an electric pump in horsepower with can lift $2000m^3$ of water from a depth of $20m$ in $25min$.($1m^3$ of water=${10}^{3}kg$, g=$10m/s^2$)

[$1HP=750watts$]

Q. The transformer ratio in the step-up transformer is

1. equal to $1$.
2. greater than $1$.
3. less than $1$.
4. less than $0$.

Q.

The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10g$and the velocity of the bullets is$600m{s}^{-1}$ , the power (in kW) of the gun is

1. $43200$

2. $432$

3. $72$

4. $7.2$

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

Q. If a force $\overrightarrow{F}=(7\hat{i}-6\hat{j}+2\hat{k})\text{N}$ and velocity $\overrightarrow{v}=(6\hat{i}+\hat{k})\text{m/s},$ then the instantaneous power is

1. $42\text{watts}$
2. $46\text{watts}$
3. $44\text{watts}$
4. $57\text{watts}$

Q.

In a hydroelectric power station, the height of the dam is 10 m. How many kg of water must fall per second on the blades of a turbine in order to generate 1 MW of electrical power? Take $g=10m{s}^{-2}$.

1. ${10}^{4}kg{s}^{-1}$

2. ${10}^{5}kg{s}^{-1}$

3. ${10}^{6}kg{s}^{-1}$

4. ${10}^{3}kg{s}^{-1}$

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. 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. Power versus time graph for a force is given below. Work done by the force upto time $t(\le t_0)$,

1. First decreases then increases
2. Always increases
3. First increases then decreases
4. Always decreases

Q.

A family uses 8 kW of power. (a) Direct solar energy is incident on the horizontal surface at an average rate of 200 W per square meter. If 20% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW? (b) Compare this
area to that of the roof of a typical house.

Q. A block of mass $m$ is located on a horizontal plane. The block acquires a horizontal velocity $v_0$ due to friction. Find the mean power developed by the friction force during the motion of the body. The frictional cofficient is $\mu =0.3,m=2\text{kg}$ and $v_0=5\text{m/s}$ (Take $g=10{\text{m/s}}^2$)

1. $30\text{watt}$
2. $45\text{watt}$
3. $60\text{watt}$
4. $15\text{watt}$

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

Q. Power versus time graph for a force is given below. Then, work done by the force upto time $t(\le t_0)$

1. first decreases then increases
2. first increases then decreases
3. always increases
4. always decreases

Q.

Define watt. Express kilowatt in terms of joule per second. A 150 kg car engine develops 500 W for each kg. What force does it exert in moving the car at a speed of $20m{s}^{-1}?$

Q. Solar insolation of a rectangular module $(1.5\text{m}\times 2.0\text{m})$ of a solar cell is $550{\text{W/m}}^2.$ If efficiency of the cell is $12\%$, what power can be drawn from cell?

1. $396\text{W}$
2. $240\text{W}$
3. $99\text{W}$
4. $198\text{W}$

Q.

A bulb is rated $100W-240V$. What is the magnitude of current drawn by the bulb?

Q. A particle of mass m moves along a circle of radius $R$ with a normal acceleration varying with time as $a_n=b{t}^2$, where b is a constant. Find the mean value of power averaged over the first 2 seconds after the beginning of motion. ($m=1,b=2,R=1$)

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 body does $50J$ of work in $5seconds$. What is its power?

Q.

The average power dissipation in pure inductance is:

1. 

2. 

3. 

4. zero

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

Q.

An unruly demonstrator lifts a stone of mass 200 g from the ground and throws it at his opponent. At the time of projection, the stone is 150 cm above the ground and has a speed of 3.00 m/s. Calculate the work done by the demonstrator during the process. If it takes one second for the demonstrator to lift the stone and throw, what horsepower does he use ?

Q.

What is the efficiency formula?

Q. A force $(2\hat{i}+3\hat{j}+\hat{k})\text{N}$ acting on a body, displaces it from $\overrightarrow{r_1}=(2\hat{i}+\hat{j}+3\hat{k})\text{m}$ to $\overrightarrow{r_2}=(8t^2\hat{i}+9t^3\hat{j}+7t\hat{k})\text{m}$. Find the instantaneous power delivered by the force at $t=1\text{sec}$.

1. $100\text{W}$
2. $60\text{W}$
3. $80\text{W}$
4. $120\text{W}$

Q.

How do you define power in terms of energy?

Q.

If the heart works 60 joules in one minute. What is its power?