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Commercial unit of energy - class-IX

Description: commercial unit of energy
Number of Questions: 35
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Tags: work and energy physics work, energy and power work and power
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A two kilowatt motor pumps out water from a well 10 meter deep. The quantity of water pumped out per hour  is ( g = 10 $m/s^2$)

  1. $72 \times 10^2$ kg

  2. $72 \times 10^3$ kg

  3. $72 \times 10^4$ kg

  4. $72 \times 10^5$ kg


Correct Option: B
Explanation:

Two kilowatt motor  pump means that 2kJ wotk is done in $1$ sec 

Let $m$ be the mass of water that is pumped out 
Work done , $W=2\ kJ=2000\ J$
Time taken , $t=1 sec$

Displacement of water , $h= 10\ m$

As in this case  $W=mgh $

$\implies 2000= m\times 10\times 10$
$\implies m=20\ kg$

Quantity of water pumped out per sec , $m=20\ kg$

$\therefore \text{ Quantity of water that is pumped out per hour }= m\times 3600=20\times 3600= 72\times 10^3 \ kg $

If the heart pushes 1 cc of blood in one second under pressure 20000 $N/m^2$ the power of heart is:

  1. 0.02 W

  2. 400 W

  3. 20 mW

  4. 0.2 W


Correct Option: A
Explanation:

Given that , 
Pressure ,$P=2000 N/m^2$
Change in Volume = $1 cc= 10^{-6 } L $

$\text{Power}=\dfrac{\text{workdone}}{\text{time}}=\dfrac{\text{pressure }\times \text{ change in volume}}{\text{time}}=\dfrac {2000\times 10^{-6}}{1}= 0.02 \ W$

The pump of a water pumping system uses $2.0\ kW$ of electrical power when raising water. The
pumping system lifts $16kg$ of water per second through a vertical height of $7.0\ m$.
What is the efficiency of the pumping system?

  1. $1.8\%$

  2. $5.6\%$

  3. $22\%$

  4. $55\%$


Correct Option: B
Explanation:

The power of pump = $\dfrac{d(mgh)}{dt}$

                                 = $(16 \times 10 \times 7 ) W$
                                  = $112 W$
So, efficiency = $\dfrac{P _{out}}{P _{in}}\times 100$
                       = $\dfrac{112}{2000} \times 100$
                       =  $5.6 %$%

Choose the correct option.

  1. kW$=$ unit of power and kWh $=$ unit of energy.

  2. kW$=$ unit of energy and kWh $=$ unit of power.

  3. kW and kWh are both of unit of energy.

  4. kW and kWh are both of unit of power.


Correct Option: A
Explanation:

Electrical Power is measured in watts (W), kilo-watts (kW), mega-watts (MW), and giga-watts (GW). The power of a load can change quickly, especially if the load is turning on and off.

Electrical Energy is measured in kilowatt-hours (kWh), megawatt-hours, and sometimes (less commonly) in watt-hours or watt-seconds. Energy is the primary measurement used by the utility company to determine your bill each month (although demand and power factor are also sometimes used). Unlike power, energy does not change quickly, but instead accumulates gradually.

In our household applications, commercial unit of electricity is used. One unit is equal to:

  1. $1\ kW$

  2. $1\ kWh$

  3. $1\ kW/h$

  4. $1\ Wh$


Correct Option: B
Explanation:

Electrical Energy is measured in kilowatt-hours (kWh). A unit is the primary measurement used by the utility company to determine your bill each month (although demand and power factor are also sometimes used). Unlike power, energy does not change quickly, but instead accumulates gradually.

$250 kg$ of water per minute is to be drawn from a well $150 m$ deep. An electric pump of _______ can be used. $(g = 10 m/s^2) $ 

  1. 6 horse power

  2. 7 horse power

  3. 8 horse power

  4. 9 horse power


Correct Option: D
Explanation:

Power, $P = \dfrac{w}{t} = \dfrac{mgh}{t} =\dfrac{mgh}{t\times 746} HP = 8.35HP$
$\therefore Power$  $= 9HP$ 

Which of the following can be used to express energy? Symbols have their usual meanings for the units of physical quantities.
(i) Wh   (ii) VC    (iii) VAs$^2$  (iv)  A$^2\Omega$s

  1. (i) , (ii)

  2. (ii), (iii), (iv)

  3. (i), (ii), (iv)

  4. (i), (ii), (iii), (iv)


Correct Option: C
Explanation:

Using   $E = Pt$       $\implies$ Energy can be expressed in $Wh$

Using  $W = qV$     $\implies$ Energy can be expressed in $VC$
Using  $H = i^2Rt$  $\implies$ Energy can be expressed in $A^2\Omega s$
Whereas  Energy cannot be expressed by  $VAs^2$
Hence option C is correct.

Electric energy supplied to homes is measured by

  1. voltmeter

  2. ammeter

  3. galvanometer

  4. kilowatt-hour meter


Correct Option: D
Explanation:

The kilowatt hour (symbolized kW⋅h as per SI) is a composite unit of energy equivalent to one kilowatt (1 kW) of power sustained for one hour. One watt is equal to 1 J/s. One kilowatt hour is 3.6 MJoules, which is the amount of energy converted if work is done at an average rate of one thousand watts for one hour.

1 kilowatt-hour is the amount of .... by 1000 watt electric appliance when it operates for one hour.

  1. Power

  2. Voltage

  3. Electric energy

  4. None


Correct Option: C
Explanation:

1 kilowatt-hour is the amount of energy energy consumed by a 1000 watt electric appliance when it is operated for one hour.

Convert 1 kWh to SI unit of energy.

  1. $3.6\times 10^6J$

  2. $3.6\times 10^8J$

  3. $1.8\times 10^6J$

  4. $1.8\times 10^8J$


Correct Option: A
Explanation:

$1\ kWh$ $ = 1000 \times 3600$ $ = 3.6\times 10^6$ $J$

Smallest commercial unit of energy is

  1. Kilowatt hour

  2. Watt second

  3. Watt hour

  4. Watt minutes


Correct Option: C
Explanation:

Smallest commercial unit of energy is called Watt hour. It is defined as the amount of electric energy, which flows through a conductor in one hour, at a power of one watt.

Convert $28.8  khJ$ into kilo watt hour.

  1. $8 \times {10}^{-3} kwh$

  2. $8 kwh$

  3. $8 \times {10}^{3} kwh$

  4. None of these


Correct Option: A
Explanation:

$E = \dfrac{28.8 \times {10}^{3}}{3.6 \times {10}^{6}}$
   $= 8 \times {10}^{-3}  kwh$

Biggest commercial unit of energy.

  1. $kwh$

  2. $BOT$

  3. $kVAh$

  4. All


Correct Option: D
Explanation:

The biggest commercial unit of energy is kilowatt hour $\left(kwh\right)$. It is also known as kilo-volt-ampere hour $\left(kVAh\right)$ and board of trade unit (BOT) or simply electric unit.

Unit used in selling electrical energy to consumer.

  1. Volt-Amper

  2. Kilowatt-hour

  3. Volt/second

  4. None


Correct Option: B
Explanation:

Commercial unit of electrical energy is  Kilowatt-hour  i.e  $kWh$ and 1 kWh is equal to 1 unit of energy.

Watt hour meter means

  1. Electric energy

  2. Current

  3. Voltage

  4. Power


Correct Option: A
Explanation:

As watt hour is the unit of energy, thus watt hour meter measures the amount of energy consumed for a given time period.

$1  kwh$ is equal to

  1. $3.6 \times {10}^{6} J$

  2. $100 J$

  3. $1000 J$

  4. $3.6 \times {10}^{3} J$


Correct Option: A
Explanation:

$1  kwh = 1  kw \times 1  h$
     $= 1000  w \times 1 \times 60 \times 60$
     $= 3.6 \times {10}^{6}  J$

A lamp rated 20w and an electric iron rated 50w are used for 2 hour everyday. Calculate the total energy consumed in 20 days.

  1. 14kwh

  2. 2.8kwh

  3. 40kwh

  4. All


Correct Option: B
Explanation:

Energy consumed by lamp in 2 hour     $E _l = 0.02\times 2 = 0.04$ kWh per day

Energy consumed by iron in 2 hour     $E _i = 0.05\times 2 = 0.1$ kWh per day
$\therefore$ Total energy consumed by both appliance     $E _T = (E _l+E _i)\times 20 = (0.04+0.1)\times 20 = 2.8$ kWh

One kilowatt hour is equal to

  1. $\displaystyle 36\times { 10 }^{ 5 }$ joules

  2. $\displaystyle 36\times { 10 }^{ 3 }$ joules

  3. $\displaystyle { 10 }^{ 3 }$ joules

  4. $\displaystyle { 10 }^{ 5 }$ joules


Correct Option: A
Explanation:

$1$ kW  $ = 1000$ $\dfrac{J}{s}$            

$1$ h $ = 3600$ s
$\therefore$  $1$ kWh $ = 1000\dfrac{J}{s}\times 3600$ $s  =36\times 10^5$  $J$

Number of KWh in 1Joule.

  1. $\displaystyle 3.6\times { 10 }^{ 6 }KWh$

  2. $\displaystyle 2.77\times { 10 }^{ -7 }KWh$

  3. $\displaystyle 600KWh$

  4. $\displaystyle 1.6\times { 10 }^{ -19 }KWh$


Correct Option: B
Explanation:

We know  $1$ kWh $ = 3.6\times 10^6$ $J$

$\therefore$  $1$ $J = \dfrac{1}{3.6\times 10^6} = 2.77\times 10^{-7}$ kWh

Calculate the number of Joules in 1KWh.

  1. $\displaystyle 6\times { 10 }^{ -19 }J$

  2. $\displaystyle 3.6\times { 10 }^{ 6 }J$

  3. $\displaystyle 60J$

  4. $\displaystyle 59J$


Correct Option: B
Explanation:

$1$ kW $ = 1000$ $\dfrac{J}{s}$

$1$ h $=3600$ s 
$\therefore$  $1$ kWh $ = 1000\dfrac{J}{s}\times 3600$ $s  =3.6\times 10^6$  $J$

When we pay for our electricity bill, we are paying for the ____________.

  1. charge used

  2. current used

  3. power used

  4. energy used


Correct Option: D
Explanation:

A unit is defined as $kWh$, means a $1000 joule/ sec$ is used for $1 hour$ ,

$1KwH=1000\times 3600=3.6\times10^6joules$
we pay for unit and that is energy 

$1kWh= $ _________?

  1. $3600000\ J$

  2. $10000\ J$

  3. $4.2\ J$

  4. $25000\ J$


Correct Option: A
Explanation:
Kilowatt hour is the energy consumed by a body of power $1\ kW$ in $1\ hr$. 
Hence, 
$1\ kWh = 1 kW \times 1\ hr$
              $=  10^3 W \times 3600\ s$
              $= 3600000\ J$

Kilowatt-hour is the unit of :

  1. potential difference.

  2. electric power.

  3. electrical energy.

  4. charge.


Correct Option: C
Explanation:

The kilowatt-hour (symbolized kWh) is a unit of energy equivalent to one kilowatt (1 kW) of power expended for one hour. The kilowatt-hour is commercially used as a billing unit for energy delivered to consumers by electric utilities.

Kilowatt hour is the unit of:

  1. Power

  2. Energy

  3. Impulse

  4. Force


Correct Option: B
Explanation:

KiloWatt is the unit of power and hour is the unit of time. Product of power and time equals Energy.

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

  1. ${t^{3/4}}$

  2. ${t^{3/2}}$

  3. ${t^{1/4}}$

  4. ${t^{1/2}}$


Correct Option: B
Explanation:

Let's consider a body is moved along a straight line by a machine delivering a constant power $P$. The distance moved by the body is $S$. 


Power, $P=F.v$.. . . . . . (1)


Force, $F=ma$ . . . . . . . .(2)

where, $v=\dfrac{S}{t}$ 

acceleration, $a=\dfrac{S}{t^2}$

$m=$ mass

from  equation (1) and equation (2), we get

$P=\dfrac{mS}{t^2}\times \dfrac{S}{t}$

$S^2=\dfrac{Pt^3}{m}$

From the above equation, we get

$S^2\propto t^3$

$S\propto t^{3/2}$

The correct option is B.

A body is moving along a straight line delivering power given as P = at, then work (W) done is given for time 0 to t is

  1. W = a

  2. W = $\frac{1}{2}a t^2$

  3. W = $2at^2$

  4. W = $a^2t^2$


Correct Option: B
Explanation:

Given that ,

Power , $P= at$
We know that 
$P=\dfrac{dW}{dt}$

$\implies \dfrac{dW}{dt}= at$

$\implies dW= at dt$
$\implies W= \int _0^t atdt$
$\implies W=\dfrac12 at^2$

$\therefore $ Work done for time 0 to t ,   $W=\dfrac12 at^2$  

A force of $ 2\hat { i } +3\hat { j } +2kN $ acts on a body for 4 s and produces a displacement of $3\hat {i} +4\hat {j} +5 \hat {k} m $ calculate the power ?

  1. 5 w

  2. 6 w

  3. 7 W

  4. 9 w


Correct Option: C
Explanation:

Given that,

Force  ,$F= 2 \hat i + 3\hat j + 2\hat k $  N
Displacement , $S= 3\hat i + 4\hat j +5 \hat k $ m 
Time Taken , $t= 4\ s$

Power, $P=\dfrac Pt = \dfrac{F\cdot S}{t}= \dfrac{6+12+10}{4}= \dfrac{28}4 = 7\ W$

A pump of $200W$ power is lifting $2kg$ water from an average depth of $10m$ in one second. Velocity of water delivered by the pump is :

$(g=10m/s^2)$

  1. $10m/s$

  2. $2m/s$

  3. $4 m/s$

  4. $1 m/s$


Correct Option: A
Explanation:

acceleration due to gravity $g = 10m/sec^2$

height $H = 10 meters$
mass $= 2kg$
Potential energy $= mgh = 2\times 10 \times 10 = 200J$
as power $= \dfrac{work \ done}{time}$
when power of motor $= 200w$
$200 = 200/t$
$\Rightarrow t = 1sec$
here displacement of water= height $= 10m$
time = 1sec
Hence,
Velocity $V= \dfrac{Displacement}{Time}$
              $V= \dfrac{10}{1}$
              $V= 10m/sec$

A small diesel engine uses a volume of $1.5 \times 10^4\, cm^3$  of fuel per hour to produce a useful power
output of 40 kW. It may be assumed that 34 kJ of energy is transferred to the engine when it uses $1.0\, cm^3$  of fuel.
What is the rate of transfer from the engine of energy that is wasted?

  1. 850 kW

  2. 920 kW

  3. 840 kW

  4. 810 kW


Correct Option: D
Explanation:

Energy produced by $1.0\ cm^3$ of fuel = $34\ kJ$

So, energy produced by  $1.5 \times 10^4\ cm^3$ of fuel in one hour = $1.5 \times 10^4 \times 34\ kJ$
                                                                                                   = $5.1 \times 10^5\ kJ$
Energy produced in one second = $\dfrac{5.1 \times 10^5}{60}\ kJ/s$
                                                         = $850\ kW$
So, rate of energy wasting = $(850-40)\ kW$
                                             = $810\ kW$

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest :

  1. at the highest position of the body

  2. at the instant just before the body hits the earth

  3. it remains constant throughout

  4. at the instant just after the body is projected


Correct Option: B
Explanation:

$Power,$ $P$ $=$$\overrightarrow{F}$.$\overrightarrow{v}$ $=$ $Fv$ $cos$$\theta$
$Just$ $before$ $hitting$ $the$ $earth$ $θ$ $=$ $0°.$ $Hence,$ $the$ $power$ $exerted$ $by$ $the$ $gravitational$ $force$ $is$ $greatest$ $at$ $the$ $instant$ $just$ $before$ $the$ $body$ $hits$ $the$ $earth.$

1 kWh is equal to

  1. $3.6 \times 10^6 MJ$

  2. $3.6 \times 10^5 MJ$

  3. $3.6 \times 10^2 MJ$

  4. $3.6 MJ$


Correct Option: D
Explanation:
1 kilowatt hour is the energy produced by 1 kilowatt  power source in 1 hour.

$1kWh=1kW\times 1hour=1000\times 3600 W.s$

$\implies 1kWh=3.6\times 10^6J$

$\implies 1kWh=3.6MJ$

Answer-(D)

Number of kilowatt-hours =$\dfrac { volt\times ampere\times time }{ 1000 } $. Then:

  1. time in seconds

  2. time in minutes

  3. time in hours

  4. time in days


Correct Option: C
Explanation:

Kilowatt-hours is the power generated in one hour=$\dfrac{volt\times current\times time( hour)}{1000}$


Answer-(C)

If 1 unit of electricity cost $0.20$, how much does it cost to switch on a heater marked $120 V$, $3 A$ for $90$ min?

  1. $ 0.11$

  2. $ 2.70$

  3. $ 64.80$

  4. $ 108.00$


Correct Option: A
Explanation:
Voltage across the heater $V = .12$ kilo-volts 
Current flowing through the heater $I = 3 A$
Thus power of the heater $P = VI$
$\therefore$ $P = 0.12 \times 3 = 0.36 $ $kW$
Time of operation $t = 90$ min $ = 1.5 $ hr
Thus energy consumed $E = Pt$
$\implies$ $E = 0.36 \times 1.5 = 0.54$ $kWhr$
Cost to switch on heater =  $0.54 \times 0.2 = 0.11$

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P _{0}$. The instantaneous velocity of this car is proportional to:

  1. $t^{1/2}$

  2. $t^{-1/2}$

  3. $t/\sqrt{m}$

  4. $t^{2}P _{0}$


Correct Option: A
Explanation:

Power =F.V


Power delivered as at 

Cont. magnitude $P _0$

$P _0=F.V$

$P _0=ma\times V$

$\dfrac{P _0}{m}=\dfrac{dv}{dt}\times V$

$\displaystyle \left(\dfrac{P _0}{m}\right)\int^t _0 dt=\int^v _0 vdv$

$\dfrac{P _0t}{m}=\dfrac{V^2}{2}$

$V^2=\left(\dfrac{2P _0}{m}\right)t$

$V=\sqrt{\dfrac{2P _0}{m}}\times t^{\dfrac{1}{2}}$

$\boxed{V\alpha\,t^{\dfrac{1}{2}}}$

$1$ kWh$=$ ______________J.

  1. $3.6\times 10^6$

  2. $36\times 10^6$

  3. $3.6\times 10^7$

  4. $3.6\times 10^5$


Correct Option: A
Explanation:

$1$ kilowatt-hour(kWh) is a unit of energy. Normally, we want energy to be expressed in joules(J) and time in seconds(s).
Energy(kWh)$=$Power(kW)$\times$(h)$=1000$W$\times 3600$s$=1000$J/s$\times 3600$s$=3600000$J$=3.6\times 10^6$J.

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