Work and Energy Test

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Work and Energy Test - 31

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Question 1
1 / -0

The velocity of a bus, moving on a smooth road, is increased from 8 m/s to 32 m/s in 120s. During this process, the potential energy of the bus

A
Does not change

B
Becomes twice that of initial potential energy

C
Becomes four times that of initial potential energy

D
Becomes sixteen times that of initial potential energy

Solution

As potential energy, $$P=mgh$$
Since, there is no vertical displacement so, $$h=0$$.
Hence, potential energy change$$P=mgh=0$$
The moving bus has only change in its Kinetic energy.
Question 2
1 / -0

Two bodies P and Q of equal masses are kept at heights $$x$$ and $$4x$$ respectively. What will be the ratio of their potential energies?

A
$$1:8$$

B
$$4:1$$

C
$$1:4$$

D
$$8:1$$

Solution

Potential energy $$P=mgh$$
Given, $$h_1=x ; h_2=4x$$

Since, the masses are same,
then $$\dfrac{P_1}{P_2}=\dfrac{h_1}{h_2} = \dfrac{x}{4x}=1:4$$
Question 3
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 4
1 / -0

What is the mass of a man if he does $$3600\ J$$ of work in climbing a tree $$6\ m$$ tall? $$({g = 10 m/s^2})$$

A
$$70\ kg$$

B
$$60\ kg$$

C
$$85\ kg$$

D
$$52\ kg$$

Solution

Work done, $$W=3600\ J$$
Height of the tree, $$h=6\ m$$
Acceleration due to gravity, $$g=10\ m/s^2$$
Mass, $$m$$

We know,
$$W=Force\times distance$$
$$W=F\times h$$
$$\implies F=\dfrac Wh$$

$$\implies F=\dfrac {3600}{6}$$

$$F=600\ N$$

Also, $$F=mg$$

$$\implies m=\dfrac {F}{g}$$

$$\implies m=\dfrac {600}{10}$$

$$m=6\ kg$$
Question 5
1 / -0

When a stone falls freely towards the earth, its total energy ?

A
First decreases and then becomes zero

B
Remains constant

C
Increases

D
Decreases

Solution

Since the ball is in free-fall, the only force acting on it is gravity. Therefore, we can use the principle of conservation of mechanical energy - initially the ball has potential energy and no kinetic energy. As it falls, its total energy (the sum of the KE and the PE) remains constant and equal to its initial PE. when reaches the ground there is no PE only KE I.E., Equal to initial PE
Hence, option B is correct.
Question 6
1 / -0

A girl weighing 50 kg makes a high jump of 1.2 m.What is her kinetic energy at the highest point? $${(g= 10 ms^{-2}}$$)

A
6000 J

B
600 J

C
60 J

D
Zero

Solution

Given,
mass of girl $$M=50\ kg\\h=1.2\ m$$
A girl is jumping vertically upward, when it will reach at maximum Hight its velocity will become zero
ie $$v_f=0$$
$$K.E=\dfrac12 mv^2=\dfrac12m\times 0=0$$
Option D
Question 7
1 / -0

A car is being driven at a constant speed of $$5\ m/s$$ by a force of $${3\times 10^8}\ N$$. It takes $$2$$ minutes to reach its destination. What is the work done?

A
$${15\times 10^8\ J}$$

B
$${18\times 10^{10}\ J}$$

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

D
$${10\times 10^8 \ J}$$

Solution

Given,
Speed, $$v=5\ m/s$$
Time taken, $$t=2\ min$$
$$t = 2 \times 60=120\ s$$
Force applied, $$F=3\times 10^8\ N$$
Displacement, $$d$$

We know,
$$v=\dfrac dt$$
$$\implies d=v\times t$$
$$d=5 \times 120$$
$$d = 600\ m$$

Work done, $$W=F \times d$$
$$W=3\times 10^8\times 600$$
$$W=18\times 10^{10}\ J$$
Question 8
1 / -0

The velocity of a ball goes on decreasing when it is thrown vertically upwards. When its velocity becomes zero, its potential energy becomes

A
Minimum

B
Maximum

C
Zero

D
9.8 J

Solution

According to the law of conservation of energy its kinetic energy is getting converted in to potential energy because of gain in height. So, if the velocity of a ball goes on decreasing when it is thrown vertically upwards. When its velocity becomes zero, its potential energy becomes maximum.
Question 9
1 / -0

A car is moving at $$100\ km/h$$. If the mass of the car is $$950\ kg$$, Its kinetic energy is:

A
$$367\ MJ$$

B
$$0.367\ MJ$$

C
$$3.67\ MJ$$

D
$$3.67\ J$$

Solution

Mass of the car, $$m=950\ kg$$
velocity of the car, $$v= 100\ km/h = { \left( 100\times \dfrac { 5 }{ 18 } \right) }$$m/s.
kinetic energy $$\displaystyle KE=\dfrac { 1 }{ 2 } \times m\times { v }^{ 2 }$$

$$\displaystyle =\frac { 1 }{ 2 } \times 950\times { \left( 100\times \frac { 5 }{ 18 } \right) }^{ 2 }J$$
$$\displaystyle =366512.35J=0.367\quad MJ$$.
Hence, the kinetic energy of the car is 0.367 MJ.
Question 10
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.

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Re-Attempt Weekly Quiz Competition

Work and Energy Test - 31

Result

Work and Energy Test - 31

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SHARING IS CARING

Question 1

Does not change

Becomes twice that of initial potential energy

Becomes four times that of initial potential energy

Becomes sixteen times that of initial potential energy

Solution

Question 2

$$1:8$$

$$4:1$$

$$1:4$$

$$8:1$$

Solution

Question 3

Zero

19.6 J

9.8 J

9800 J

Solution

Question 4

$$70\ kg$$

$$60\ kg$$

$$85\ kg$$

$$52\ kg$$

Solution

Question 5

First decreases and then becomes zero

Remains constant

Increases

Decreases

Solution

Question 6

6000 J

600 J

60 J

Zero

Solution

Question 7

$${15\times 10^8\ J}$$

$${18\times 10^{10}\ J}$$

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

$${10\times 10^8 \ J}$$

Solution

Question 8

Minimum

Maximum

Zero

9.8 J

Solution

Question 9

$$367\ MJ$$

$$0.367\ MJ$$

$$3.67\ MJ$$

$$3.67\ J$$

Solution

Question 10

A man walking on the road

A man climbing a hill

A man lying on his bed

A man running in the garden.

Solution

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