Tag: work and power

Questions Related to work and power

A force F acting on a body depends on its displacement $S$ as $F \propto S^{1/3}$. The power delivered by $F$ will depend on displacement as:

power work and power work, energy and power physics energy and its forms

  1. $S^{2/3}$

  2. $S^{-5/3}$

  3. $S^{1/2}$

  4. $S^0$

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Correct Option: A
Explanation:

We know Power=$\dfrac{work \ done}{time}$

Also work done = Force $\times$displacement

As given $F \ \alpha \ {S}^{1/3}$

$F=KS^{ 1/3 }$------(1) (where $K$= constant of proportionality)

Now Power= $\dfrac{F \times S}{time}$----(2)
Putting value of 1 in 2 we get 

$P= {\dfrac{KS^{\dfrac{2}{3}}}{t}}$

An engine of ine metric ton is going up an inclined plane, 1 in 2 at the rate of 36 kmph. If the coefficient of friction is $1/ \sqrt{3}$, the power of engine is 

power work and power work, energy and power physics energy and its forms

  1. 9.8W

  2. 98W

  3. 980W

  4. 98kW

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Correct Option: D

A train of mass $6 \times 10^2$ metric tones is pulled by a locomotive. The speed of the train will be $36 \,kmhr^{}-1$. The locomotive pulls the train on the train on the level track, whose mass is $125$ metric tones. The force of friction acts on the locomotive and the train is $1 \times 10^1$ newton per metric tonne. Calculate the power of the locomotive.

power work and power work, energy and power physics energy and its forms

  1. 72500

  2. 6000

  3. 5000

  4. 4000

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Correct Option: A
Explanation:

$m = 600$
$m\ell = 125$
$m \,net = 725$
$f = \dfrac{10}{tan}$
$t _{net} = 10 \times 125$

$V = 36 \,km/h = 36 \times \dfrac{5}{18} m/s$

$P = t _{net} \times V = 72500 \,W$

The power of water pump is The power of water pump is  $4kW.$  If  $\left( g=10{ m }{ { s }^{ -2 } } \right) ,$  the amount of water it can raise in $1$ minute to a height of $20 m$  is then

power work and power work, energy and power physics energy and its forms

  1. $100$ litre

  2. $1000$ litre

  3. $1200$ litre

  4. $2000$ litre

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Correct Option: C
Explanation:

Given that,

Power, $P=4\,kW=4000\,W$

Height, $h=20\,m$

Time, $t=60\,\sec $

$ power=\dfrac{work}{time} $

$ 4000=\dfrac{mgh}{t} $

$ 4000=\dfrac{m\times 10\times 20}{60} $

$ m=1200\,Kg $

The pump can raise 1200 litre in one minute

An object of mass accelerates uniformly from rest to a speed $v _f$ in time $t _f$ Then the instantaneous power delivered to the object,as a function of time $t$ is -

power work and power work, energy and power physics energy and its forms

  1. $mt\left(\dfrac{{v _f}^2}{t _f}\right)$

  2. $mt\dfrac{v _f}{t _f}$

  3. $\dfrac{1}{2}mt^2\left(\dfrac{v _f}{t _f}\right)^2$

  4. $\dfrac{1}{2}mt^2\left(\dfrac{v _f}{t _f}\right)$

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Correct Option: A

A force applied by the engine of a train of mass 2.05 x $10^{6} kg$ changes its velocity from 5 $ms^{-1}$ to 25  $ms^{-1}$ in 5 minutes. The power of the engine is then

power work and power work, energy and power physics energy and its forms

  1. 1.025 MW

  2. 2.05 MW

  3. 5 MW

  4. 6 MW

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Correct Option: B
Explanation:

Given that,

Mass of train, $m=2.05\times {{10}^{6}}\,Kg$

Time, $t=5\,\min utes=300\,s$

$ v=25\,m/s $

$ u=5\,m/s $

Acceleration,

$ a=\dfrac{v-u}{t} $

$ a=\dfrac{25-5}{300} $

$ a=\dfrac{2}{30}=\dfrac{1}{15}\,m/{{s}^{2}} $

Using equation of motion,

$ {{v}^{2}}-{{u}^{2}}=2as $

$ {{(25)}^{2}}-{{(5)}^{2}}=2\times \dfrac{1}{15}\times s $

$ s=4500\,m $

Power,

$ P=\dfrac{work\,\,done}{time} $

$ P=\dfrac{F\times d}{t} $

$ P=\dfrac{m\times a\times s}{t} $

$ P=\dfrac{2.05\times {{10}^{6}}\times 1\times 4500}{15\times 300} $

$ P=2.05\times {{10}^{6}}\,W $

$ P=2.05\,MW $

A motor lifts $100 kg$ of water in $2 min$ from a well of $60m$ depth then the electric power of the motor is$(Taken g=10 m/s^2)$

power work and power work, energy and power physics energy and its forms

  1. $1000 W$

  2. $750 W$

  3. $1200 W$

  4. $500W$

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Correct Option: D
Explanation:

A motor lifts $=100kg$ of water

Time $=2min=2\times60=120s$
Depth$=60m$ depth then,
electric power of the motor$=?$
Taking $=10m/s^2$
$P=Power=\cfrac{mgh}{t}\ \quad=\cfrac{100\times10\times60}{120}\ \quad=500W$

A force $'F'$ accelerates a block of mass $'m'$ along a straight line to velocity $'v'$ from rest and displace it through a distance $'s'$. What is the average power developed?

power work and power work, energy and power physics energy and its forms

  1. $\dfrac {v^{2}}{2F}$

  2. $Fv$

  3. $\dfrac {mv^{2}}{2s}$

  4. $\dfrac {Fv}{2}$

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Correct Option: D

The average power required to lift a 100 Kg mass trough a highest of 50 meters in approximatley 50 second would be

power work and power work, energy and power physics energy and its forms

  1. 50 J/s

  2. 5000 J/s

  3. 100 J/s

  4. 980 J/s

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Correct Option: D

A pump ejects $12000kg$ of water at speed of $4m/s$ in $40$ second. Find the average rate at which the pump is working

power work and power work, energy and power physics energy and its forms

  1. $0.24KW$

  2. $2.4KW$

  3. $24KW$

  4. $24W$

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Correct Option: B