A circular disc is rolling on a horizontal surface. Its total kinetic energy is $600\,J$. Its rotational kinetic energy is:
A. 200 J
B. 400 J
C. 300 J
D. 100 J
Last updated date: 26th Mar 2023
•
Total views: 207.3k
•
Views today: 5.84k
Answer
207.3k+ views
Hint:Kinetic energy is an energy which a body possesses by virtue of being in motion. Moving object or particle depends not only on motion but also on its mass. Kinetic energy is a property of a moving object or a particle depends not only on its motion but also on its mass. Kinetic energy defined as the work is needed to be accelerating a body of a given mass.
Complete step by step answer:
Assuming the kinetic energy of rotational and kinetic energy of translation in total kinetic energy. That means, $K.{E_{total}} = K.{E_{rotati}} + K.{E_{trans}}$. Here kinetic energy in rotational is the center of mass into moment of inertia and angular velocity.
That is $\dfrac{1}{2}{I_c}{\omega ^2}$
The kinetic energy in translation is mass of object and center of velocity,
That is $\dfrac{1}{2}m{V_c}^2$
The total kinetic energy is,
$K.{E_{total}} = \dfrac{1}{2}I{\omega ^2} + \dfrac{1}{2}m{V^2}$
Here the total kinetic energy is 600 joules, and moment of inertia is $\dfrac{{m{R^2}}}{4}$and angular velocity $\omega = \dfrac{V}{R}$ by substituting all the values in kinetic total energy we get,
$600 = \dfrac{1}{2}m{V^2} + \dfrac{1}{2}\dfrac{{m{R^2}}}{2} \times \dfrac{{{V^2}}}{{{R^2}}} \\
\Rightarrow 600 = \dfrac{1}{2}m{V^2} + \dfrac{{m{V^2}}}{4} \\
\Rightarrow 600 = \dfrac{{3m{V^2}}}{4} \\
\Rightarrow m{V^2} = 600 \times \dfrac{4}{3} \times \dfrac{1}{2} \\
\Rightarrow m{V^2} = 400J \\ $
The total kinetic energy is the sum of rotational kinetic energy and translational kinetic energy. Thus the translational kinetic energy is 400 Joules. Then rotational kinetic energy is the difference if total kinetic and translational kinetic energy,
That is,
$K.{E_{rotati}} = K.{E_{total}} - K.{E_{trans}} \\
\Rightarrow K.{E_{rotati}} = 600 - 400 \\
\therefore K.{E_{rotati}} = 200\,J \\ $
Hence, the rotational kinetic energy is 200 joules and the correct option is A.
Note:An object is the energy that it possesses due to its motion; it is defined as the work needed to accelerate the body of a mass. The Circular disc on a horizontal surface and its rotational kinetic energy is about 200 joules. Kinetic energy S.I unit is in joules.
Complete step by step answer:
Assuming the kinetic energy of rotational and kinetic energy of translation in total kinetic energy. That means, $K.{E_{total}} = K.{E_{rotati}} + K.{E_{trans}}$. Here kinetic energy in rotational is the center of mass into moment of inertia and angular velocity.
That is $\dfrac{1}{2}{I_c}{\omega ^2}$
The kinetic energy in translation is mass of object and center of velocity,
That is $\dfrac{1}{2}m{V_c}^2$
The total kinetic energy is,
$K.{E_{total}} = \dfrac{1}{2}I{\omega ^2} + \dfrac{1}{2}m{V^2}$
Here the total kinetic energy is 600 joules, and moment of inertia is $\dfrac{{m{R^2}}}{4}$and angular velocity $\omega = \dfrac{V}{R}$ by substituting all the values in kinetic total energy we get,
$600 = \dfrac{1}{2}m{V^2} + \dfrac{1}{2}\dfrac{{m{R^2}}}{2} \times \dfrac{{{V^2}}}{{{R^2}}} \\
\Rightarrow 600 = \dfrac{1}{2}m{V^2} + \dfrac{{m{V^2}}}{4} \\
\Rightarrow 600 = \dfrac{{3m{V^2}}}{4} \\
\Rightarrow m{V^2} = 600 \times \dfrac{4}{3} \times \dfrac{1}{2} \\
\Rightarrow m{V^2} = 400J \\ $
The total kinetic energy is the sum of rotational kinetic energy and translational kinetic energy. Thus the translational kinetic energy is 400 Joules. Then rotational kinetic energy is the difference if total kinetic and translational kinetic energy,
That is,
$K.{E_{rotati}} = K.{E_{total}} - K.{E_{trans}} \\
\Rightarrow K.{E_{rotati}} = 600 - 400 \\
\therefore K.{E_{rotati}} = 200\,J \\ $
Hence, the rotational kinetic energy is 200 joules and the correct option is A.
Note:An object is the energy that it possesses due to its motion; it is defined as the work needed to accelerate the body of a mass. The Circular disc on a horizontal surface and its rotational kinetic energy is about 200 joules. Kinetic energy S.I unit is in joules.
Recently Updated Pages
Which element possesses the biggest atomic radii A class 11 chemistry JEE_Main

The highly efficient method of obtaining beryllium class 11 chemistry JEE_Main

Which of the following sulphates has the highest solubility class 11 chemistry JEE_Main

Amongst the metal Be Mg Ca and Sr of group 2 of the class 11 chemistry JEE_Main

Which of the following metals is present in the greencolored class 11 chemistry JEE_Main

To prevent magnesium from oxidation in the electrolytic class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE
