Work and Energy Test

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Work and Energy Test - 57

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Weekly Quiz Competition

Question 1
1 / -0

A body is falling a height $$h$$. After it has fallen a height $$\dfrac{h}{2}$$. it will possess

A
only potential energy

B
only kinetic energy

C
half potential energy and half kinetic energy

D
more kinetic and less potential energy

Solution

$$(c)$$ half potential and half kinetic energy
Explanation: When the body is height $$h$$; its potential energy is at maximum and kinetic energy is zero. When the body hits the ground, its potential energy becomes zero and kinetic energy is at maximum. At mid-way i.e., half the height; its potential energy becomes half of the maximum potential energy and same happens to the kinetic energy.
Question 2
1 / -0

The height of the water dam in the hydroelectric power station is $$20$$ m. How much water. in $$1$$ second, should fall on turbine, so that $$1$$ MW power is generated ?($$g = 10m/s^2$$)

A
$$5000\,kg$$

B
$$10000\,kg$$

C
$$500\,kg$$

D
$$7,500\,kg$$

Solution

We know that,
$$Power(P)=\Bigg(\dfrac{\text{Work Done}}{\text{Time taken}}\Bigg)$$

$$\text{work done} = mgh$$

$$\therefore P=\dfrac{mgh}{t}$$

$$g = 10\ ms^{-2}$$
$$h = 20\ m$$
$$time = 1\ s$$

$$\Rightarrow 1 \times 10^6=\dfrac{m(10)(20)}{1}$$

$$\Rightarrow m=5000\,kg$$
Question 3
1 / -0

The engine of a car of mass $$1500$$ kg. keeps the car moving with constant velocity $$v=5\ m/s$$. If frictional force is $$1000$$ N, the power of the engine is...

A
$$5\,kW$$

B
$$7.5\,kW$$

C
$$15\,kW$$

D
$$75\,kW$$

Solution

Given,
Frictional force, $$F=1000\,N$$
To keep the car running at constant speed the engine must apply same amount of force as friction.

$$Power=\dfrac{\text{Work done}}{\text{Time taken}}=\dfrac{F \times S}{t}$$

$$\Rightarrow P=F \times \Bigg(\dfrac{S}{t}\Bigg)=Fv$$

$$\Rightarrow P=1000 \times 5=5000\,W=5\,kW$$
Question 4
1 / -0

Four alternatives are given to each of the following incomplete statements/questions. Choose the right answer:
Which of the following object has higher potential energy?

A
mass $$ = 10\,kg$$ , $$ g = 9.8\, ms^{-2} , h = 10\,m $$

B
mass $$ = 5\,kg , g = 9.8\, ms^{-2} , h = 12\,m $$

C
mass $$ = 8\,kg , g = 9.8\,ms^{-2} , h = 100\,m $$

D
mass $$ = 6\,kg , g = 9.8\,ms^{-2} , h = 20\,m $$

Solution

The potential energy is given as-
$$PE = mgH$$
$$m$$; mass of the object
$$g = 9.8/ ms^{-2}$$
$$h$$; height gained from ground

For option A:
$$m = 10\ kg,\ h = 10\ m$$
$$PE = 10 \times 9.8 \times 10$$
$$\Rightarrow PE = 980\ J$$

For option B:
$$m = 5\ kg,\ h = 12\ m$$
$$PE = 5 \times 9.8 \times 12$$
$$\Rightarrow PE = 588\ J$$

For option C:
$$m = 8\ kg,\ h = 100\ m$$
$$PE = 8 \times 9.8 \times 100$$
$$\Rightarrow PE = 7840\ J$$

For option D:
$$m = 6\ kg,\ h = 20\ m$$
$$PE = 6 \times 9.8 \times 20$$
$$\Rightarrow PE = 1176\ J$$

For option C potential energy is highest so option C is the correct answer.
Question 5
1 / -0

Work done is equal to?

A
Change in kinetic energy

B
Kinetic energy

C
Acceleration

D
None of these

Solution

The work done is equal to the change in the kinetic energy of an object, hence option $$A$$ is correct.
Question 6
1 / -0

Is the work required to be done by an external force on an object on a frictionless, horizontal surface to accelerate it from a speed $$v$$ to a speed $$2v$$.

A
equal to the work required to accelerate the object from $$v = 0$$ to $$v$$,

B
twice the work required to accelerate the object from $$v = 0$$ to $$v$$

C
three times the work required to accelerate the object from $$v = 0$$ to $$v$$,

D
four times the work required to accelerate the object from $$0$$ to $$v$$

E
not known without knowledge of the acceleration

Solution

Answer (c). The net work needed to accelerate the object from $$v = 0$$ to $$v$$ is
$$W_{1}=KE_{1f}-KE_{1i}=\dfrac{1}{2}mv^{2}-\dfrac{1}{2}m(0)^{2}=\dfrac{1}{2}mv^{2}$$
The work required to accelerate the object from speed $$v$$ to speed $$2v$$ is
$$W_{2}=KE_{2f}-KE_{2i}=\dfrac{1}{2}m(2v)^{2}-\dfrac{1}{2}mv^{2}$$
$$=\dfrac{1}{2}m(4v^{2}-v^{2})=3\left ( \dfrac{1}{2}mv^{2} \right )=3W_{1}$$
Question 7
1 / -0

At the start of the free-fall of an object from height $$h$$, the potential energy is _____ and kinetic energy is _____.

A
Zero, $$mgh$$

B
$$mgh$$, infinite

C
Infinite, $$mgh$$

D
$$mgh$$, zero

Solution

Given,
At the start of the free-fall of an object from height $$h$$
Initial velocity, $$v=0$$ (at rest)
Acceleration due to gravity, $$g$$
Let the mass of the object be $$m$$

Potential energy, $$U=mgh$$
Kinetic energy, $$KE=\dfrac 12mv^2$$
$$KE=\dfrac 12m(0)^2$$

$$KE=0$$
Question 8
1 / -0

Bullet $$2$$ has twice the mass of bullet $$1$$. Both are fired so that they have the same speed. If the kinetic energy of bullet $$1$$ is $$K$$, is the kinetic energy of bullet $$2$$

A
$$0.25K$$

B
$$0.5K$$

C
$$0.71K$$

D
$$K$$

E
$$2K$$

Solution

Let $$m$$ be the mass of bullet $$1$$.
According to the given condition, the mass of bullet $$2$$ is $$2m.$$
Kinetic energy of bullet $$1$$ is $$KE_1=\dfrac{1}{2}mv^2=K$$
KE of bullet $$2$$ is $$KE_2=\dfrac{1}{2}(2m)v^2=2(\dfrac{1}{2}mv^2)=2K$$
Question 9
1 / -0

We can explain free-fall of an object on the basis of?

A
Work-energy theorem

B
Conservation of Kinetic energy

C
Conservation of potential energy

D
Conservation of energy

Solution

According to the law of conservation of energy, energy can only be converted from one form to another; it can neither be created or destroyed. The total energy before and after the transformation remains the same. The law of conservation of energy is valid in all situations and for all kinds of transformations for example, the free-fall of an object.

When a body starts falling, it posses only potential energy. As it falls, its potential energy decreases and converts into kinetic energy . Finally, at the lowest point, it has only kinetic energy. So, during free fall, the body converts potential energy into kinetic energy.But the sum of $$KE$$ and $$PE$$ at any instant during the fall will be same .Hence total energy is conserved.
Question 10
1 / -0

Whenever energy gets transformed, the total energy_______.

A
Varies with time

B
Varies with position

C
Remains unchanged

D
None of these

Solution

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Re-Attempt Weekly Quiz Competition

Work and Energy Test - 57

Result

Work and Energy Test - 57

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SHARING IS CARING

Question 1

only potential energy

only kinetic energy

half potential energy and half kinetic energy

more kinetic and less potential energy

Solution

Question 2

$$5000\,kg$$

$$10000\,kg$$

$$500\,kg$$

$$7,500\,kg$$

Solution

Question 3

$$5\,kW$$

$$7.5\,kW$$

$$15\,kW$$

$$75\,kW$$

Solution

Question 4

mass $$ = 10\,kg$$ , $$ g = 9.8\, ms^{-2} , h = 10\,m $$

mass $$ = 5\,kg , g = 9.8\, ms^{-2} , h = 12\,m $$

mass $$ = 8\,kg , g = 9.8\,ms^{-2} , h = 100\,m $$

mass $$ = 6\,kg , g = 9.8\,ms^{-2} , h = 20\,m $$

Solution

Question 5

Change in kinetic energy

Kinetic energy

Acceleration

None of these

Solution

Question 6

equal to the work required to accelerate the object from $$v = 0$$ to $$v$$,

twice the work required to accelerate the object from $$v = 0$$ to $$v$$

three times the work required to accelerate the object from $$v = 0$$ to $$v$$,

four times the work required to accelerate the object from $$0$$ to $$v$$

not known without knowledge of the acceleration

Solution

Question 7

Zero, $$mgh$$

$$mgh$$, infinite

Infinite, $$mgh$$

$$mgh$$, zero

Solution

Question 8

$$0.25K$$

$$0.5K$$

$$0.71K$$

$$K$$

$$2K$$

Solution

Question 9

Work-energy theorem

Conservation of Kinetic energy

Conservation of potential energy

Conservation of energy

Solution

Question 10

Varies with time

Varies with position

Remains unchanged

None of these

Solution

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