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How are Joule (J) and ergs (erg) related?

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Important Questions on Work, Energy and Power

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If the engine of a train of mass

2.05 \times 10^{6} kg

requires a duration of

7

minutes for changing its velocity from

5 m \cdot s^{- 1}

25 m \cdot s^{- 1},

find the power of the engine.

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Water is pumped steadily out of a flooded basement, at the speed of

10 m s^{- 1}

through a hose (tube) of radius,

1 cm,

passing through a window,

3 m

above the water level. The power of the pump is (Assume

g = 10 m s^{- 2}

, density of water

= 1000 kg m^{- 3}

)

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A machine gun fires

360

bullets per minute. Each bullet travels with velocity of

500 m s^{- 1}

. If the power of the machine gun is

4.5 kW

then the mass of each bullet is:

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A machine gun fires five bullets per second into a target. The mass of each bullet is

5 gm

. If the average force required to hold the gun in position is

12.5 N

, then what is the speed (S in

m s^{- 1}

) of each bullet & what is the power (

P

kW

) delivered to each bullet?

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A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time

t

is proportional to

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A quarter horse power motor runs at a speed of

600 rpm .

Assuming

60 %

efficiency, the work done by the motor in one rotation is

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An engine develops

20 kW

of power. How much time will it take to lift a mass of

200 kg

to a height of

40 m ? (g = 10 m s^{- 2})

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A particle of mass

m

is moving in a circular path of constant radius

r

such that its centripetal acceleration

a_{c}

is varying with time

t

a_{c} = k^{2} r t^{2}

, where

k

is a constant. The power delivered to the particle by the force acting on it is -

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A body of mass

m

accelerates uniformly from rest to

v_{1}

in the time

t_{1}

. The instantaneous power delivered to the body as a function of time

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A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time

t

is proportional to :-

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A car of mass '

m = 1500 kg

' starts from rest and accelerates such that its instantaneous velocity is proportional to

\sqrt{t}

, where t is time in seconds. What should be the instantaneous power delivered to the car if its instantaneous velocity is

20 m s^{- 1}

after

10

seconds.

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The heart of a man pumps

5

litres of blood through the arteries per minute at a pressure of

150 mm

of mercury. If the density of mercury be

13.6 \times 10^{3} k g m^{- 3}

and

g = 10 m s^{- 2}

, then the power of heart in watt is:

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Water falls from a

40 m

high dam at the rate of

9 \times 10^{4} kg

per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of

100 W

lamps, that can be lit, is
(Take

g = 10 {m s}^{- 2}

)

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A water pump rated

600 W,

has an efficiency of

95 % .

If it is used to raise water through vertical distance of

60 m .

The volume of water drawn in

20

minutes, is [Use density of water

= 1000 kg m^{- 3}, g = 10 m / s^{2}

]

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The energy that will be ideally radiated by a

100 kW

transmitter in

1

hour is

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A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time '

t

' is proportional to

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A body of mass

2 kg

is driven by an engine delivering a constant power of

1 J s^{- 1}

. the body starts from rest and moves in a straight line. After

9 s

, the body has moved a distance (in

m

)….

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

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A body of mass

1 kg

begins to move from rest under the action of a time dependent force

\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}) N

, where

\hat{i}

and

\hat{j}

are unit vectors along x and y axis. What power will be developed by the force at the time t?

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Water falls down a

500.0 m

shaft to reach a turbine which generates electricity. How much water must fall per second in order to generate

1.00 \times 10^{9}

watts of power ? (Assume

50 %

efficiency of conversion and

g = 10 m s^{- 1}

)

How are Joule (J) and ergs (erg) related?

Important Questions on Work, Energy and Power

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