Work and Energy Test

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Work and Energy Test - 49

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Weekly Quiz Competition

Question 1
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Directions For Questions

A body of mass $$2\ kg$$ starts from rest and moves with uniform acceleration. It acquires a velocity $$20\ ms^{-1}$$ in $$4\ s$$

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The power exerted on the body at $$2\ s$$ is:

A
$$50\ W$$

B
$$100\ W$$

C
$$150\ W$$

D
$$200\ W$$
Question 2
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A man of mass 20 kg is running in a straight line with velocity 10 m/s. What is value of his kinetic energy?

A
$$10\ J$$

B
$$100\ J$$

C
$$1000\ J$$

D
$$10000\ J$$

Solution

The kinetic energy of the particle is given as-
$$K.E. = \dfrac{1}{2}mv^2$$
$$m$$; mass of the object
$$v$$; speed of the object
$$\Rightarrow K.E. = \dfrac{1}{2} \times 20 \times 10^2J$$
$$\Rightarrow K.E. = 1000 J$$
Question 3
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Two bodies traveling with velocity $$20ms^{-1}$$ and $$40ms^{-1}$$ have same K.E. If the mass of the body having velocity $$40ms^{-1}$$ is 8 kg the mass of other body is

A
8 Kg

B
16 kg

C
24 kg

D
32 kg

Solution

Given
$$ V_1 = 20 m/s$$ and $$ V_2 = 40 m/s$$
$$ M_2 = 8\ kg $$

$$K.E_1 = K.E_2$$
$$\dfrac{1}{2}M_1V_1^2 = \dfrac{1}{2}M_2V_2^2 $$
$$\implies M_1 = M_2 \times \dfrac{V_2^2}{V_1^2} = 8\times \dfrac{40^2}{20^2} = 32\ kg$$
Question 4
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Two men $$A$$ and $$B$$ each weighing $$80\ kg$$, run up the same stair case. While $$A$$ does it in $$20\ s, B$$ does it in $$15\ s$$. The ratio of the powers developed by $$A$$ and $$B$$ is

A
$$\dfrac{4}{3}$$

B
$$\dfrac{3}{4}$$

C
$$\dfrac{1}{2}$$

D
$$\dfrac{1}{4}$$

Solution

We know $$Power=\dfrac{work }{time}$$
work done by both the men is the same = Gain in potential energy = $$m\times g\times h $$
$$m,g,h$$are same for both so work same for both.
So $$P \propto \dfrac{1}{t}$$
Therefore $$\dfrac{P_{a}}{P_{b}}=\dfrac{t_{b}}{t_{a}} \implies\dfrac{P_{a}}{P_{b}}=\dfrac{15}{20}$$=$$\dfrac{3}{4}$$
Hence Option B is correct
Question 5
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How much height must an object of mass $$5kg$$ be lifted to have potential energy $$5000J$$ ?$$[g=10 m/s^2]$$

A
$$100m$$

B
$$50m$$

C
$$120m$$

D
$$110m$$

Solution

Gravitation potential energy is given by $$P.E = mgh $$
Given:
Mass $$m=5 \ kg$$
$$g=10 \ m/s^2$$
$$5000 = 5 \times 10 \times h $$
$$ \implies h = 100 m$$
Question 6
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A car is accelerated on a levelled road and attains a speed of $$5$$ times its initial speed. In this process , the kinetic energy of the car:

A
does not change

B
becomes $$4$$ times that of initial kinetic energy

C
becomes $$8$$ times that of initial kinetic energy

D
becomes $$25$$ times that of initial kinetic energy

Solution

Lets initial velocity of car is $$v$$, final velocity of this car will be $$5\ v$$
$$K.E = \dfrac{1}{2}$$ $$ mv ^{2}$$
$$\therefore \ K.E\propto v^2$$
$$K.E_{f}=K.E_i \left(\dfrac{v_f}{v_i}\right)^2$$ where $$f$$ stand for final and $$i$$ for initial.

$$K.E_{f}=K.E_i \left(\dfrac{5v}{v}\right)^2=25\ K.E_i$$

So, when the speed increases to 5 times of its initial velocity, the kinetic energy will become 25 times.

The correct answer is d) becomes $$25$$ times that of initial kinetic energy
Question 7
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A stone is thrown upwards as shown in the diagram. When it reaches $$P,$$ which of the following has the greatest value for the stone?

A
its acceleration

B
its kinetic energy

C
its potential energy

D
its weight

Solution

P is the highest point of the ball during its motion. At this point, its speed will be zero. This makes the kinetic energy to be zero. The acceleration remains constant all through the motion and the weight depends on the value of acceleration due to gravity. So weight will also be constant.

So, the correct answer is c) its potential energy.
Question 8
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No work is done when:

A
a nail is hammered into a wooden box

B
a box is pushed along horizontal floor

C
there is no component of force, parallel to the direction of motion

D
none of these

Solution

The formula for work done when the force is applied at an angle to the direction of motion is given by,
$$W = FS \,cos \theta$$
When there will be no component of force, parallel to the direction of motion then force F in direction of motion is zero, so work done will also be zero.
Question 9
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Potential energy of a person is minimum when:

A
Person is standing

B
Person is sitting on a chair

C
Person is sitting on the ground

D
Person is lying on the ground

Solution

Potential energy of a body is defined as energy of a body due to its position in gravitational field.
In general,
Potential energy $$= M \times g \times h$$ where: h is the height above ground.
If the person will be lying on ground then it will have minimum height above the ground therefore potential energy of the person will also be minimum.
Question 10
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When a stone of mass 'm' falls through a vertical height 'd', the decrease in the gravitational energy is:

A
$$mg/d$$

B
$$mg^2/2$$

C
$$mgd$$

D
$$md/g$$

Solution

Potential energy stored in a body of mass m and at height 'd' will be given by $$m \times g \times d$$
This gravitational potential energy keeps on decreasing with the decrease in height of stone, and when the stone falls completely, this potential energy is lost . So when object loses height $$d $$ the corresponding loss in potential Energy is $$= mgd$$

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Re-Attempt Weekly Quiz Competition

Work and Energy Test - 49

Result

Work and Energy Test - 49

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SHARING IS CARING

Question 1

$$50\ W$$

$$100\ W$$

$$150\ W$$

$$200\ W$$

Question 2

$$10\ J$$

$$100\ J$$

$$1000\ J$$

$$10000\ J$$

Solution

Question 3

8 Kg

16 kg

24 kg

32 kg

Solution

Question 4

$$\dfrac{4}{3}$$

$$\dfrac{3}{4}$$

$$\dfrac{1}{2}$$

$$\dfrac{1}{4}$$

Solution

Question 5

$$100m$$

$$50m$$

$$120m$$

$$110m$$

Solution

Question 6

does not change

becomes $$4$$ times that of initial kinetic energy

becomes $$8$$ times that of initial kinetic energy

becomes $$25$$ times that of initial kinetic energy

Solution

Question 7

its acceleration

its kinetic energy

its potential energy

its weight

Solution

Question 8

a nail is hammered into a wooden box

a box is pushed along horizontal floor

there is no component of force, parallel to the direction of motion

none of these

Solution

Question 9

Person is standing

Person is sitting on a chair

Person is sitting on the ground

Person is lying on the ground

Solution

Question 10

$$mg/d$$

$$mg^2/2$$

$$mgd$$

$$md/g$$

Solution

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