Work Energy and Power Test

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Work Energy and Power Test - 29

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Weekly Quiz Competition

Question 1
1 / -0

Which one of the following possesses potential energy?

A
Moving vehicle on the road

B
A running athlete

C
Stone on the road

D
A stretched rubber band

Solution

Moving vehicle on the road possesses kinetic energy.

A running athlete possesses kinetic energy.

Stone on the road possesses kinetic energy.

A stretched rubber band possesses potential energy.

Hence, option D is correct.
Question 2
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An overhead tank having some water possesses .......... energy.

A
Kinetic

B
Potential

C
Thermal

D
Electrical

Solution

We know that Potential energy is the energy possessed by a body by the virtue of its position.
$$\therefore$$ An overhead tank having some water possesses Potential energy, as it is at a height.
Question 3
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Law of conservation of energy states that:

A
energy cannot be destroyed but can be created and transformed from one form to another

B
energy exists in only one form

C
energy exists in many forms but it cannot be transformed

D
energy can neither be created nor be destroyed but can be transformed from one form to another

Solution

Law of conservation of energy states that: energy can neither be created nor be destroyed but can be transformed from one form to another
Question 4
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Energy possessed by a body by virtue of its motion is :

A
Potential energy

B
Kinetic energy

C
Chemical energy

D
Electrical energy

Solution

Kinetic energy is defined as the energy possessed by a body by virtue of its motion. and it is equal to $$ K.E. = \cfrac{1}{2}mv^{2} $$ Where $$m$$ and $$v$$ are mass and Velocity of moving body.
Question 5
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A student sitting at the top of a tree has ............ than the student who is sitting on the ground.

A
less potential energy

B
more potential energy

C
more kinetic energy

D
more gravitational energy

Solution

Potential energy = $$mgh$$
$$m\rightarrow mass$$
$$g\rightarrow acceleration\ due\ to\ gravity$$
$$h\rightarrow height\ from\ ground$$
P.E. is directly proportional to the height from the ground. Hence a student sitting at the top of a tree has more potential energy than the student who is sitting on the ground.
Question 6
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The form of energy present in a wound spring is:

A
chemical

B
heat energy

C
magnetic

D
mechanical

Solution

Potential energy is stored in a wound spring. Potential energy is a type of mechanical energy. Hence, energy present in a wound spring is mechanical energy.
Question 7
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The energy directly related to the speed of a moving body and its mass is:

A
Kinetic

B
Potential

C
Solar

D
Electric

Solution

The kinetic energy of a body is the energy by virtue of its motion.
$$ K.E = \dfrac{1}{2}mv^2 $$
where $$m$$ is mass and $$v$$ is velocity.

Hence, Kinetic energy is directly related to the speed of a moving body and its mass.
Question 8
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A boy holds a pendulum in his hand while standing at the edge of a circular platform of radius $$r$$ rotating at an angular speed $$\omega$$. The pendulum will hang at an angle $$\theta$$ with the verticle such that

A
$$\;tan\,\theta=0$$

B
$$\;tan\,\theta=\displaystyle\frac{\omega^2r^2}{g}$$

C
$$\;tan\,\theta=\displaystyle\frac{r\omega^2}{g}$$

D
$$\;tan\,\theta=\displaystyle\frac{g}{\omega^2r}$$

Solution

A pseudo force $$(ma_r)$$ acts on the bob due to the rotation of circular platform.
In bob's frame, the bob is at rest (or equilibrium).
$$\therefore$$ $$T sin \theta = ma_r$$ where $$a_r = rw^2$$
$$\implies$$ $$T sin\theta = mrw^2$$ ........(1)

Also $$T cos\theta =mg$$ ..........(2)
Divide (2) by (1) we get, $$tan\theta =\dfrac{rw^2}{g}$$
Question 9
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A particle of mass $$'m'$$ describes a circle of radius $$(r)$$. The centripetal acceleration of the particle is $$\displaystyle\frac{4}{r^2}$$. The momentum of the particle:

A
$$\;\displaystyle\frac{2m}{r}$$

B
$$\;\displaystyle\frac{2m}{\sqrt{r}}$$

C
$$\;\displaystyle\frac{4m}{r}$$

D
$$\;\displaystyle\frac{4m}{\sqrt{r}}$$

Solution

Centripetal acceleration of the particle, $$a = \dfrac{v^2}{r}$$
$$\therefore$$ $$\dfrac{4}{r^2}= \dfrac{v^2}{r} $$ $$\implies v = \dfrac{2}{\sqrt{r}}$$
Thus the momentum of the particle, $$P = mv = \dfrac{2m}{\sqrt{r}}$$
Question 10
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A mass tied to a string moves in a vertical circle with a uniform speed of $$5\;m/s$$ as shown. At the point $$P$$ the string breaks. The mass will reach a height above $$P$$ of nearly: $$(g=10\ m/s^{2})$$

A
$$\;1\;m$$

B
$$\;0.5\;m$$

C
$$\;1.75\;m$$

D
$$\;1.25\;m$$

Solution

Given : $$u =5 m/s$$ $$a = - g = -10 m/s^2$$
When the string breaks at point P, from there onwards the mass has the free falling motion.
At the maximum height attained, the velocity of the mass is zero i.e $$v = 0 m/s$$
Using $$v^2 - u^2 = 2aS$$
$$\therefore$$ $$ 0 - 5^2 = 2 (-10) h$$ $$\implies h = 1.25$$ m