Tag: work, energy and power

Questions Related to work, energy and power

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

A refrigerator transfer 180 joule of energy in one second from temperature $ { -3 }^{ 0 }C$ to $ { 27 }^{ 0 }C.$ Calculate the average power consumed, assuming no energy losses in the process. 

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

  1. 18 W

  2. 54 W

  3. 20 W

  4. 120 W

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Correct Option: A

A man pulls a lawn roller with a force of $20\ kgf$. He applies the force at an angle $60^{\circ}$ with the ground through $10\ m$. If he takes $1$ minutes in doing so, calculate the power developed.

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

  1. $25\ J$

  2. $16.67\ J$

  3. $34\ J$

  4. $58\ J$

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Correct Option: B

If the average power radiated by the star is $10 ^ { 16 } \mathrm { W }$ , the deuteron supply of the star is exhausted in a time of the order of 

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

  1. $10 ^ { 6 }$ seccond

  2. $10 ^ { 14 }$ second

  3. $10 ^ { 12 }$ second

  4. $10 ^ { 16 }$ second

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Correct Option: C

A boat moving with constant speed v in still waters experiences a total frictional force F. The power developed by the boat is

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

  1. $\frac{1}{2}Fv$

  2. $Fv$

  3. $\frac{1}{2}Fv^2$

  4. $Fv^2$

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Correct Option: B

A body of mass m is projected at an angle $\displaystyle \theta $ with the horizontal with an initial velocity $\displaystyle v _{0}.$ The average power of gravitational force over the whole time of flight is

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

  1. $\displaystyle mg\cos \theta $

  2. $\displaystyle \frac{1}{2}mg\sqrt{u\cos \theta }$

  3. $\displaystyle \frac{1}{2}mgu\sin \theta $

  4. zero

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Correct Option: D
Explanation:

The projected body again comes back down. Hence the net displacement in the vertical direction will be 0.
$\therefore W=mgh=mg\times 0=0$

A time varying power $P=2t$ is applied on a particle of mass $m$. Find average power over a time interval from t=0 to t=t :

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

  1. $\displaystyle P _{av}= t$

  2. $\displaystyle P _{av}= 2t$

  3. $\displaystyle P _{av}= 4t$

  4. $\displaystyle P _{av}= 8t$

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Correct Option: A
Explanation:
Average power over a time interval $t=0$ to $t=t$ is 
$\dfrac{\int _0^tPdt}{\int _0^tdt}$
$=\dfrac{\int _0^t 2tdt}{t}$
$=\dfrac{t^2}{t}=t$

A car of mass 1000 kg accelerates from rest to $100 : km : h^{-1}$ in 5 seconds. What is the average power of the car ?

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

  1. $7.71\times 10^5 W$

  2. $7.71\times 10^4 W$

  3. $15.42\times 10^4 W$

  4. $15.42\times 10^5 W$

Show answer
Correct Option: B
Explanation:


Mass of the car m$=1000\ kg$
Initial velocity of car ${v} _{1}=0$
Final velocity of car ${v} _{2}$$=100km/h=100\times\dfrac{5}{18}m/s=27.78m/s$
Average power of car$=$change in kinetic energy per unit time$=\dfrac{\dfrac{1}{2}m{{v} _{2}}^{2}-\dfrac{1}{2}m{{v} _{1}}^{2}}{t}$,since ${v} _{1}=0$
So,average power of car$=\dfrac{\dfrac{1}{2}m{{v} _{2}}^{2}}{t}$
                                 $=\dfrac{\dfrac{1}{2}\times1000\times{27.78}^{2}}{5}$
                                 $=7.71\times{10}^{4}W$
                                

A particle of mass $m$ is lying on smooth horizontal table. A constant force $F$ tangential to the surface is applied on it. Find average power over a time interval from $t=0$ to $t=t$.

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

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

  2. $\displaystyle \frac{F^{2}t}{2m}$

  3. $\displaystyle \frac{2F^{2}t}{3m}$

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

Show answer
Correct Option: B
Explanation:

Average power of a time interval $t=0$ to $t=t$


is $\dfrac{\int^t _0 Fvdt}{ _0^t\int dt}$


$=\dfrac{F\int _0^t vdt}{t}$

$=\dfrac{F\int _0^t \dfrac{F}{m}tdt}{t}$

$=\dfrac{F^2t}{2m}$