Work and Energy Test

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Work and Energy Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

A force applied by an engine of a train of mass $$ 2.05 \times 10^6 \ kg $$ changes it velocity from $$ 5 \ m /s $$ to $$ 25\ m/s $$ in $$ 5\ minutes$$. The power of engine is

A
$$ 1.025 \ MW $$

B
$$ 2.05 \ MW $$

C
$$ 5 \ MW $$

D
$$ 6 \ MW $$

Solution

Given,
Mass of train $$=2.05\times 10^6\ kg$$
Initial velocity $$u=5\ m/s$$
Final velocity $$v=25\ m/s$$
Time required $$t=5\ mint= 5\times 60\ s=300\ s$$
From conservation of energy,
Work done by engine $$=$$ change in kinetic energy of the train
$$W=K.E_f-K.E_i$$
$$Power$$ = $$ \dfrac {work\ done}{time} = \dfrac {\dfrac {1}{2} m(v^2 -u^2) }{t} $$

$$ P = \dfrac {1}{2} \times \dfrac { 2.05 \times 10^6 \times [ (25)^2 -(5^2) ]}{ 5 \times 60 } $$

$$ P = 2.05 \times 10^6 W = 2.05 MW $$
Question 2
1 / -0

A car of mass 1000 kg accelerates uniformly from rest to a velocity of 54 km/hour in 5s. The average power of the engine during this period in watts is (neglect friction)

A
$$ 2000 \quad W $$

B
$$ 22500 \quad W $$

C
$$ 5000 \quad W $$

D
$$ 2250 \quad W $$

Solution

Power $$ = \dfrac {Work done}{time} = \dfrac { Increase\ in\ K.E.}{time} $$

$$ P = \dfrac { \frac {1}{2} mv^2}{t} = \dfrac {\frac {1}{2} \times 10^3 \times (15)^2}{5} = 22500 W $$
Question 3
1 / -0

An electric lamp is marked $$60 \ W$$, $$230 \ V$$. The cost of $$1 \ kilowatt-hour$$ of power is $$Rs \ 1.25$$. The cost of using this lamp for $$8 \ hours$$ is

A
$$Rs. \ 1. 20$$

B
$$ Rs. \ 4. 00$$

C
$$Rs. \ 0. 25$$

D
$$Rs. \ 0. 60$$

Solution

Total energy consumed is given as $$E=P\times t$$
where $$P$$ is power and $$t$$ is time for which it is used.
Given, $$P=60\,W$$ and $$t=8\,h$$
$$E = 60 \times 8 \ Wh=\dfrac{60\times 8}{1000} = 0.48 \ kWh $$

Given that, cost of $$1 \ kWh$$ is $$Rs. \ 1.25$$

Hence, total cost is $$ \text{Cost}=0.48\times 1.25 = Rs. \ 0.6 $$
Question 4
1 / -0

The power of pump, which can pump $$200 \ kg$$ of water to a height of $$50 \ m$$ in $$10 \ sec$$, will be

A
$$ 10 \times 10^3 \quad watt $$

B
$$ 20 \times 10^3 \quad watt $$

C
$$ 4 \times 10^3 \quad watt $$

D
$$ 60 \times 10^3 \quad watt $$

Solution

$$ Power \ P = \dfrac {Work \ done}{time} = \dfrac { mgh}{t} = \dfrac { 200 \times 10 \times 50}{10} = 10 \times 10^3 W $$
Question 5
1 / -0

The spring will have maximum potential energy when

A
it is pulled out

B
it is compressed

C
both (a) and (b)

D
neither (a) nor (b)

Solution

The spring will have maximum potential energy when it is pulled out or compressed in.
Question 6
1 / -0

Kilowatt hour is unit of

A
Energy

B
Power

C
Impulse

D
Force

Solution

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.
Question 7
1 / -0

When spring is compressed its potential energy........

A
Remains constant

B
Reduces

C
Increases

D
Nothing can be said about it.

Solution

When a spring is compressed or stretched, potential energy energy of the spring increases in both the cases. This is because work is done by us in compression as well as stretching.
Question 8
1 / -0

Masses of two bodies are $$1$$ kg and $$4$$ kg respectively. If their kinetic energies are in $$2:1$$ proportion, the ratio of their speeds is .........

A
$$2\sqrt{2}:1$$

B
$$1:\sqrt{2}$$

C
$$1:2$$

D
$$2:1$$

Solution

We know that,
$$K.E.=\dfrac{1}{2}mv^2$$
$$m_1=1kg$$ $$m_2=4kg$$

$$\therefore \dfrac{K_1}{K_2}=\Bigg(\dfrac{m_1}{m_2}\Bigg)\Bigg(\dfrac{v_1}{v_2}\Bigg)^2$$

$$\Rightarrow \dfrac{2}{1}=\Bigg(\dfrac{1}{4}\Bigg)\Bigg(\dfrac{v_1}{v_2}\Bigg)^2$$

$$\Rightarrow \Bigg(\dfrac{v_1}{v_2}\Bigg)^2=\dfrac{8}{1}$$

$$\Rightarrow \Bigg(\dfrac{v_1}{v_2}\Bigg)=\dfrac{2\sqrt{2}}{1}$$
Question 9
1 / -0

Some children were trying to find out which of three bulbs was brightest. Which one of these gives the best start toward finding the answer?

A
"One bulb looks the brightest to me, so I already know the answer."

B
"It would help if we had a way to measure the brightness of a light bulb."

C
"All the bulbs look bright to me, so there cannot be an answer."

D
"We can take a vote and each person will vote for the bulb he or she thinks is the brightest ."

Solution

Brightness of a ball can be measured and so in turn which can be used to Judge which bulb will light the brightest.
Question 10
1 / -0

Calculate the energy possessed by a stone of mass $$10\ kg$$ kept at a height of $$5\ m$$.
Take $$g = 9.8\ m/s^{2}$$

A
$$196\ J $$

B
$$49\ J $$

C
$$490\ J $$

D
$$980\ J $$

Solution

The energy that stone may posses = kinetic energy + potential energy
Since, stone at rest $$(v = 0)$$
$$KE=\frac{mv^2}{2}$$ So kinetic energy=0
$$ \therefore $$ Total energy = Potential energy
$$(E) = mgh $$ [$$m$$ : mass , $$h$$ : height , $$g$$ : gravity ]

$$m = 10\ kg, g = 9.8\ m/s^{2} $$
and $$h = 5\ m $$
$$E = mgh = 10 \times 9.8 \times 5 $$ Joules
$$ = 490\ J $$

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Re-Attempt Weekly Quiz Competition

Work and Energy Test - 51

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Work and Energy Test - 51

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SHARING IS CARING

Question 1

$$ 1.025 \ MW $$

$$ 2.05 \ MW $$

$$ 5 \ MW $$

$$ 6 \ MW $$

Solution

Question 2

$$ 2000 \quad W $$

$$ 22500 \quad W $$

$$ 5000 \quad W $$

$$ 2250 \quad W $$

Solution

Question 3

$$Rs. \ 1. 20$$

$$ Rs. \ 4. 00$$

$$Rs. \ 0. 25$$

$$Rs. \ 0. 60$$

Solution

Question 4

$$ 10 \times 10^3 \quad watt $$

$$ 20 \times 10^3 \quad watt $$

$$ 4 \times 10^3 \quad watt $$

$$ 60 \times 10^3 \quad watt $$

Solution

Question 5

it is pulled out

it is compressed

both (a) and (b)

neither (a) nor (b)

Solution

Question 6

Energy

Power

Impulse

Force

Solution

Question 7

Remains constant

Reduces

Increases

Nothing can be said about it.

Solution

Question 8

$$2\sqrt{2}:1$$

$$1:\sqrt{2}$$

$$1:2$$

$$2:1$$

Solution

Question 9

"One bulb looks the brightest to me, so I already know the answer."

"It would help if we had a way to measure the brightness of a light bulb."

"All the bulbs look bright to me, so there cannot be an answer."

"We can take a vote and each person will vote for the bulb he or she thinks is the brightest ."

Solution

Question 10

$$196\ J $$

$$49\ J $$

$$490\ J $$

$$980\ J $$

Solution

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