Work Energy and Power Test

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Work Energy and Power Test - 59

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Weekly Quiz Competition

Question 1
1 / -0

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 2
1 / -0

Directions For Questions

A block of mass $$2\ m$$ collides elastically with a mass $$m$$ kept at rest. Friction exists between the block $$B$$ and surface with coefficient $$\mu =0.3$$, whereas no friction exists between block $$A$$ and the surface.

...view full instructions

The block will again collide after time:

A
$$6\ sec$$

B
$$4\ sec$$

C
$$8\ sec$$

D
$$\infty$$

Solution
Question 3
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Directions For Questions

A block of mass $$2\ m$$ collides elastically with a mass $$m$$ kept at rest. Friction exists between the block $$B$$ and surface with coefficient $$\mu =0.3$$, whereas no friction exists between block $$A$$ and the surface.

...view full instructions

How many collision are possible between the blocks?

A
$$2$$

B
$$4$$

C
$$27$$

D
$$infinite$$

Solution

As the distance keeps on decreasing and there will be a deceleration in the blocks .

In further results, collision increases frequently many times and slowly come in contact.

So infinite collision possible between the blocks.
Question 4
1 / -0

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 5
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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 $$= mgd$$
Question 6
1 / -0

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 7
1 / -0

A car is accelerated on a leveled road and attains a velocity $$4$$ times its initial velocity. In this process, the potential energy of the car:

A
Does not change

B
Becomes twice to that of initial

C
Becomes $$4$$ times that of initial

D
Becomes $$16$$ times that of initial

Solution

Potential energy depends on the height at which the object is situated. Where potential energy is measured by the product of the mass of the object, gravity, and height. In this case, there is no change in height of the object. Hence, there is no change in its potential energy.
Question 8
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An object of mass $$5 \,kg$$ falls from a height of $$5 \,m$$ above the ground. The loss of potential energy of the mass is:

A
$$250 \,J$$

B
$$25 \,J$$

C
$$2.5 \,kJ$$

D
$$50 \,J$$

Solution

Given,
$$Mass = 5 \,kg$$
$$Height = 5 \,m$$
Let $$g = 10 \,ms^{-2}$$
Potential energy stored in a body of mass m and height h will be given by
$$= m \times g \times h$$
$$= 5 \,kg \times 10 \,ms^{-2} \times 5 \,m$$
$$= 250 \,J$$
When the mass falls completely, same potential energy is lost $$= 250 \,J$$
Question 9
1 / -0

When a boy triples his speed, his kinetic energy becomes

A
half

B
double

C
nine times

D
no charge

Solution

Given that, speed of particle is becoming 3 times of its initial value while moving. ie $$v'=3v$$
As we know $$K.E = \dfrac{1}{2}$$ $$ mv ^{2}$$ ..........(1)
After velocity tripled $$K.E' = \dfrac{1}{2}$$ $$ m(3v) ^{2}=\dfrac92mv^2$$...........(2)
From equation 1 and 2
$$K.E' = 9 \times K.E$$
When a boy tripled his speed, his kinetic energy will becomes nine times.
Question 10
1 / -0

A position dependent force $$ F = 7 - 2x + 3x^2 $$ newton acts on a small body of mass $$2 $$ kg displace it from $$ x = 0$$ to $$ x = 5 m $$ the work done in joules is

A
$$ 70 $$

B
$$ 270 $$

C
$$ 35 $$

D
$$ 135 $$

Solution

It is known that $$W=\int Fdx$$

$$ W = \int^5_0 Fdx = \int^5_0 ( 7- 2x +3x^2) dx$$

$$W = [ 7x - x^2 + x^3]^5_0 $$

$$ W= 35 -25 + 125 = 135 J $$

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Re-Attempt Weekly Quiz Competition

Work Energy and Power Test - 59

Result

Work Energy and Power Test - 59

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SHARING IS CARING

Question 1

$$100m$$

$$50m$$

$$120m$$

$$110m$$

Solution

Question 2

$$6\ sec$$

$$4\ sec$$

$$8\ sec$$

$$\infty$$

Solution

Question 3

$$2$$

$$4$$

$$27$$

$$infinite$$

Solution

Question 4

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 5

$$mg/d$$

$$mg^2/2$$

$$mgd$$

$$md/g$$

Solution

Question 6

Person is standing

Person is sitting on a chair

Person is sitting on the ground

Person is lying on the ground

Solution

Question 7

Does not change

Becomes twice to that of initial

Becomes $$4$$ times that of initial

Becomes $$16$$ times that of initial

Solution

Question 8

$$250 \,J$$

$$25 \,J$$

$$2.5 \,kJ$$

$$50 \,J$$

Solution

Question 9

half

double

nine times

no charge

Solution

Question 10

$$ 70 $$

$$ 270 $$

$$ 35 $$

$$ 135 $$

Solution

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