Work Energy and Power Test

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Work Energy and Power Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

Find out work done by applied force to slowly extend the spring from x to 2x.

A
$$\dfrac{1}{2}kx^2$$

B
$$\dfrac{3}{2}kx^2$$

C
$$\dfrac{5}{2}kx^2$$

D
$$\dfrac{7}{2}kx^2$$

Solution

Initially the spring is extended by x
$$W\, =\, \vec{F}\, .\, \vec{ds}$$
$$W\, =\,\displaystyle \int_k^{2x}Kx.dx$$
$$W\, =\,\left [ \displaystyle \frac{Kx^2}{2} \right ]_x^{2x} \,=\,\displaystyle \frac{3}{2}Kx^2$$
It can also found by difference of PE.
i.e.

$$U_f\, =\,\displaystyle \frac{1}{2}K(2x)^2\, =\,2Kx^2\, \quad\,

\Rightarrow\, \quad\, U_i\, =\, \displaystyle \frac{1}{2}Kx^2\, \quad\,

\Rightarrow\, \quad\, U_f\, -\, U_i\, =\, \displaystyle

\frac{3}{2}Kx^2$$
Question 2
1 / -0

How fast should a girl of 40 kg run so that her kinetic energy is 320J?

A
64 m/s

B
8 m/s

C
16 m/s

D
4 m/s

Solution

Given, mass $$m=40kg , K.E=320J , v=?$$
$$K.E=\dfrac{1}{2}mv^2$$

$$320=\dfrac{1}{2}\times 40v^2$$

$$v^2=\dfrac{640}{40}=16$$

$$v=4m/s$$
So, the girl of $$40$$ $$kg$$ should run at $$4m/s$$ so that her kinetic energy is $$320J.$$
Question 3
1 / -0

How much work should be done on a car of mass 1000 kg to increase its speed from 10 m/s to 20 m/s (Ignore air resistance and friction).

A
200000 J

B
250000 J

C
150000 J

D
50000 J

Solution

We know that the work done is the change in kinetic energy.

Thus, $$W=\dfrac{1}{2}mv_f^2-\dfrac{1}{2}mv_i^2=\dfrac{1}{2}\times 1000[20^2-10^2]=15000 J$$
Question 4
1 / -0

Which one of the following possesses both kinetic and potential energies?

A
A man walking on the road

B
A man climbing a hill

C
A man lying on his bed

D
A man running in the garden.

Solution

Kinetic energy is due to motion of the object and potential energy is due to relative position of object wrt earth.
In option A. Relative position is same so no potential energy if we assume reference as level of road( assuming horizontal road), but have kinetic energy as the man is in motion.
In option C he is lying on bed so neither relative change in position nor body in motion so have none of the energies kinetic or potential.
In option D this is same case as that of option A. (assuming level park).
But in option B, man is climbing a hill so relative position wrt ground level changes so it gain some potential energy and also he is moving so also have kinetic energy .
So best possible answer is option B.
Question 5
1 / -0

An object of mass 500 g falls from a height of 2m. If $${g = 9.8 m/s^2}$$, what is its kinetic energy just before touching the ground?

A
Zero

B
19.6 J

C
9.8 J

D
9800 J

Solution

We know,
Acceleration, $$ a = \dfrac{v^2-u^2}{2s} $$
where $$v$$ and $$u$$ are final and initial velocities respectively & $$s$$ is the displacement.

Here, $$ g = \dfrac{v^2-u^2}{2h}. $$ Also, $$u=0$$
$$\implies$$ Velocity when it touches ground, $$v=\sqrt{2gh} $$

$$v=\sqrt{2gh}=\sqrt{2\times9.8\times2}$$

$$K.E=\dfrac{1}{2}mv^2=\dfrac{1}{2}\times\dfrac{500}{1000}\times (\sqrt{2\times9.8\times2})^2$$ $$=\dfrac{1}{2}\times\dfrac{500}{1000}$$$$\times2\times9.8\times2=9.8J$$
Question 6
1 / -0

A wound watch spring has ______ energy.

A
Mechanical

B
Kinetic

C
Potential

D
Kinetic and potential

Solution

The energy possessed by a body due to its change in position or shape is called the potential energy. A wound watch has potential energy.
Question 7
1 / -0

If the speed of a motor car becomes six times, then the kinetic energy becomes

A
6 times

B
36 times

C
12 times

D
24 times

Solution

Kinetic energy, K.E = $$\dfrac{1}{2}$$mv$$^{2}$$

If speed becomes 6 times, then
New K.E = $$\dfrac{1}{2}$$m (6v)$$^{2}$$ = $$\dfrac{1}{2}$$m x 36 v$$^{2}$$ = 36 x ($$\dfrac{1}{2}$$mv$$^{2}$$) = 36 x K.E

Hence, kinetic energy becomes 36 times.
Question 8
1 / -0

The spring of the winding knob of a watch has

A
mechanical energy

B
only kinetic energy

C
only potential energy

D
kinetic or potential energy

Solution

We know that total energy is kinetic energy plus potential energy.

Now, kinetic energy is

$$E=\frac { 1 }{ 2 } M{ V }^{ 2 }$$

Which depends on velocity. In watch there is no displacement in the knob, hence velocity is zero. So there is no kinetic energy. Only potential energy is there.
Question 9
1 / -0

You lift a suitcase from the floor and keep it on the table. The work done by you on the suitcase depends on

A
the path taken by the suitcase

B
your weight

C
the weight of the suitcase

D
the time taken by you in doing so

Solution

The work done by a person in lifting an object is stored as its potential energy $$mgh$$.
Hence, work done depends on the weight of the object $$mg$$.
Thus option C is correct.
Question 10
1 / -0

The work done in lifting 1 kg mass to a height of 9.8 m is about

A
1 J

B
9.8 J

C
$$(9.8)^2 J$$

D
$$\displaystyle \frac{1}{(9.8)^2} J$$

Solution

The work done in lifting an object is stored as its potential energy.
Mass of object $$m = 1$$ kg
Height upto which it is lifted $$h = 9.8$$ m
Hence work done $$W= m g h = 1 \times 9.8 \times 9.8 = (9.8)^2 J$$
Thus option C is correct.

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Work Energy and Power Test - 32

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Work Energy and Power Test - 32

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SHARING IS CARING

Question 1

$$\dfrac{1}{2}kx^2$$

$$\dfrac{3}{2}kx^2$$

$$\dfrac{5}{2}kx^2$$

$$\dfrac{7}{2}kx^2$$

Solution

Question 2

64 m/s

8 m/s

16 m/s

4 m/s

Solution

Question 3

200000 J

250000 J

150000 J

50000 J

Solution

Question 4

A man walking on the road

A man climbing a hill

A man lying on his bed

A man running in the garden.

Solution

Question 5

Zero

19.6 J

9.8 J

9800 J

Solution

Question 6

Mechanical

Kinetic

Potential

Kinetic and potential

Solution

Question 7

6 times

36 times

12 times

24 times

Solution

Question 8

mechanical energy

only kinetic energy

only potential energy

kinetic or potential energy

Solution

Question 9

the path taken by the suitcase

your weight

the weight of the suitcase

the time taken by you in doing so

Solution

Question 10

1 J

9.8 J

$$(9.8)^2 J$$

$$\displaystyle \frac{1}{(9.8)^2} J$$

Solution

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