Work and Energy Test

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Work and Energy Test - 43

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Weekly Quiz Competition

Question 1
1 / -0

A body of mass 6 kg is under a force of 6 N which causes displacement in it given by $$S =\frac{t^2}{4}$$ where 't' is time in seconds. The work done by the force in 2 s is:

A
12 J

B
9 J

C
6 J

D
3 J

Solution

$$time = t = 2s$$
$$ displacement = S=\dfrac{t^2}{4}=\dfrac{2^2}{4}=1\ m $$

The work done, $$W= force\times displacement =F \times S=6 \times 1=6\ J$$
Question 2
1 / -0

When the force retards the motion of a body, the work done is:

A
Zero

B
Negative

C
Positive

D
Positive or negative depending upon the magnitude of force and displacement

Solution

Force acting opposite to the direction of the displacement retards the motion of the body. Work done is negative when the force acts opposite to the direction of displacement.
Question 3
1 / -0

An air conditioner is rated 240 V, 1.5 kW. The air conditioner is switched on 8 hours each day. What is electrical energy consumed in 30 days?

A
2.88 kWh

B
360 kWh

C
120 kWh

D
240 kWh

Solution

Given,
Power of air conditioner $$P=1.5kW$$
Time to use per day $$t=8\ hr$$
Time to use in 30 days $$T=8\times 30\ hr$$

Energy consumed $$E=Power\times time =1.5\ kW\times 8\times 30\ hr=360kWh $$
Option B
Question 4
1 / -0

The correct formula to find the velocity of a body with kinetic energy '$$k$$' is:

A
$$V=\dfrac{2k}{m}$$

B
$$V=\sqrt{\dfrac{2k}{m}}$$

C
$$V=\dfrac{4{k}^{2}}{m}$$

D
$$V=\dfrac{1}{2}km$$

Solution

Kinetic energy of a body is given by
$$k=\dfrac{1}{2}mv^2$$

$$v^2$$ = $$\dfrac{2k}{m}$$

$$v=\sqrt {\dfrac{2k}{m}}$$.

Hence, answer is option B.
Question 5
1 / -0

A $$2kg$$ object is moving at $$3m/s$$. A $$4N$$ force is applied in the direction of motion and then removed after the object has travelled an additional $$5m$$. The work done by this force is:

A
$$10 J$$

B
$$15 J$$

C
$$20 J$$

D
$$25 J$$

Solution

intial velocity $$u=3m/s$$
final velocity $$v^2=u^2+2as=3^2+(2 \times 2 \times 5)=29$$ $$\implies v=5.3m/s$$

$$KE=\dfrac{1}{2}m(v^2-u^2)=\dfrac{1}{2} \times 2 \times {((5.3)^2-3^2)}=20J$$
Question 6
1 / -0

$$1$$ kilowatt hr $$=$$ __________ joules.

A
$$10.6 \times {10}^{6}$$

B
$$3.6 \times {10}^{6}$$

C
$$30.6 \times {10}^{6}$$

D
$$3.6 \times {10}^{5}$$

Solution

$$kWh$$ is the commercial unit of energy.
$$1\ kWh =1\times 1000\times 3600 = 3.6\times 10^6$$ joules
Question 7
1 / -0

$$1 Wh$$ (Watt hour) is equal to :

A
$$36\times { 10 }^{ 5 }J$$

B
$$36\times { 10 }^{ 4 }J$$

C
$$3600 J$$

D
$$3600 { Js }^{ -1 }$$

Solution

Watt is a unit of power such that $$1W =1\dfrac{J}{s}$$
Also we know $$1h = 3600$$ $$s$$
$$\therefore$$ $$1Wh = 1\dfrac{J}{s} \times 3600 $$ $$s = 3600$$ $$J$$
Question 8
1 / -0

A bicyclist comes to a skidding stop in $$10 m$$. During this process, the force on the bicycle due to the road is $$200N$$ and is directly opposed to the motion. The work done by the cycle on the road is

A
$$+ 2000J$$

B
$$200J$$

C
$$zero$$

D
$$20,000J$$

Solution

Work done by the road on the cycle is
$$W =F \times s=- 200N \times 10m=-2000J$$
Negative sign indicates that the direction of the force and the displacement is opposite.

The cycle applies an equal and opposite force on the road. But as the displacement of the road is zero, work done by the cycle on the road is $$zero$$.
Question 9
1 / -0

Kinetic energy of a body depends upon its:

A
mass

B
velocity

C
density

D
both A and B

Solution

Kinetic energy of the body $$K = \dfrac{1}{2}mv^2$$
$$\implies$$ $$K \propto m$$ and $$K\propto v^2$$
Thus kinetic energy of a body depends on the mass of the body as well as its velocity.
Question 10
1 / -0

A block of weight $$W$$ is pulled a distance $$l$$ along a horizontal table. The work done by the weight is

A
$$Wl$$

B
$$Wgl$$

C
$$Wl/g$$

D
zero

Solution

Here the weight will act in a vertically downward direction but the displacement is in the horizontal direction. They are perpendicular to each other. Since, there is no displacement in the direction of the weight W, work done by the weight (W) will be zero.
Hence the correct answer is option $$D $$.

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Re-Attempt Weekly Quiz Competition

Work and Energy Test - 43

Result

Work and Energy Test - 43

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SHARING IS CARING

Question 1

12 J

9 J

6 J

3 J

Solution

Question 2

Zero

Negative

Positive

Positive or negative depending upon the magnitude of force and displacement

Solution

Question 3

2.88 kWh

360 kWh

120 kWh

240 kWh

Solution

Question 4

$$V=\dfrac{2k}{m}$$

$$V=\sqrt{\dfrac{2k}{m}}$$

$$V=\dfrac{4{k}^{2}}{m}$$

$$V=\dfrac{1}{2}km$$

Solution

Question 5

$$10 J$$

$$15 J$$

$$20 J$$

$$25 J$$

Solution

Question 6

$$10.6 \times {10}^{6}$$

$$3.6 \times {10}^{6}$$

$$30.6 \times {10}^{6}$$

$$3.6 \times {10}^{5}$$

Solution

Question 7

$$36\times { 10 }^{ 5 }J$$

$$36\times { 10 }^{ 4 }J$$

$$3600 J$$

$$3600 { Js }^{ -1 }$$

Solution

Question 8

$$+ 2000J$$

$$200J$$

$$zero$$

$$20,000J$$

Solution

Question 9

mass

velocity

density

both A and B

Solution

Question 10

$$Wl$$

$$Wgl$$

$$Wl/g$$

zero

Solution

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