Work and Energy Test

Result

Work and Energy Test - 53

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Weekly Quiz Competition

Question 1
1 / -0

Two bodies $$A$$ and $$B$$ have masses $$20\ kg$$ and $$5\ kg$$ respectively. If they acquire the same kinetic energy. Find the ratio of thier velocities.

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

B
$$2$$

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

D
$$\dfrac {5}{6}$$

Solution

Given:

$$m_{A} = 20 kg$$

$$m_{B} = 5 kg$$

Kinetic Energy of both bodies A and B are the same.

Thus,

$$\dfrac{1}{2} m_{A} V_{A}^{2} = \dfrac{1}{2} m_{B} V_{B}^{2} \\$$

$$\dfrac{V_{A}^{2}}{V_{B}^{2}} = \dfrac{m_{B}}{m_{A}} \\$$

$$\dfrac{V_{A}^{2}}{V_{B}^{2}} = \dfrac{5}{20}\\$$

$$\dfrac{V_{A}}{V_{B}} = \dfrac{1}{2}$$

So, option A is correct.
Question 2
1 / -0

If increase in linear momentum of a body is 50%, then change in its kinetic energy is

A
25%

B
125%

C
150%

D
50%

Solution
Question 3
1 / -0

A man displaces a block by $$5\ cm$$ on a rough surface $$(\mu=0.5)$$ by applying a force $$50\ N$$ acting at $$37^{o}$$ to the horizontal. The work done by the applied force is

A
$$200\ J$$

B
$$100\ J$$

C
$$150\ J$$

D
$$50\ J$$

Solution
Question 4
1 / -0

A block of mass $$10kg$$ is moving in x-direction with a constant speed of $$10m/sec$$. It is subjected to a force $$F=-0.1x $$ Joules/meter during its travel from $$x=20$$ meters to $$x=30$$ meters. Its final kinetic energy will be-

A
$$475$$ joules

B
$$450$$ joules

C
$$275$$ joules

D
$$250$$ joules

Solution
Question 5
1 / -0

A small solid sphere of mass $$m$$ is released from a point $$A$$ at a height $$h$$ above the bottom of a rough track as shown in the figure. If the sphere rolls down the track without slipping, its rotational kinetic energy when it comes to the bottom of track is

A
$$mgh$$

B
$$\cfrac{10}{7}mgh$$

C
$$\cfrac{5}{7}mgh$$

D
$$\cfrac{2}{7}mgh$$

Solution
Question 6
1 / -0

A worker lifts a $$20.0 kg$$ bucket of concrete from the ground up to the top of a $$20.0 m$$ tall building. What is the amount of work that the worker did in lifting the bucket?

A
$$3.92 kJ $$

B
$$400 J$$

C
$$ 560 kJ $$

D
$$ 4.08 J $$

Solution

Given:
The mass of the bucket $$m=20\ kg$$
The height of the building $$h=20\ m$$
$$\text{Work done by the worker} = \text{Potential energy of bucket at the top of the building}$$

$$\therefore W = mgh$$

$$\Rightarrow W = 20 \times 9.8 \times 20$$

$$\Rightarrow W = 3920\;{\rm{J}}$$

Thus, the required work done is $$3.92\;k{\rm{J}}$$
Question 7
1 / -0

A solid sphere of mass $$4kg$$ and radius $$1m$$ is rotating about the given axis $$xx'$$ with angular velocity $$10rad/s$$ shown in figure. The $${K.E}_{rotation}$$ is given by

A
$$180J$$

B
$$200J$$

C
$$240J$$

D
$$280J$$

Solution
Question 8
1 / -0

The average kinetic energy of an idea gas per molecule at $$25^{o}C$$, will be

A
$$6.1\times10^{-20}J$$

B
$$6.1\times10^{-21}J$$

C
$$6.1\times10^{-22}J$$

D
$$6.1\times10^{-23}J$$

Solution
Question 9
1 / -0

Three equal resistances each of $$10\Omega $$ are connected. The maximum power consumed by each resistor is $$20W$$. the maximum power consumed by the system is

A
60 W

B
30 W

C
15 W

D
13.3 W
Question 10
1 / -0

Two spring of spring constant k and 3k are stretched separately by same force. The ratio of the potential energy stored in them respectively will be

A
3 : 1

B
9 : 1

C
1 : 3

D
1 : 9

Solution