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
Answer
282.9k+ 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
Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Which of the following would not be a valid reason class 11 biology CBSE

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What is meant by monosporic development of female class 11 biology CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which one of the following places is unlikely to be class 8 physics CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

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

Elucidate the structure of fructose class 12 chemistry CBSE

What is pollution? How many types of pollution? Define it
