
A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy ( ) as well as rotational kinetic energy ( ) simultaneously. The ratio :( ) for the sphere is?
A- 10:7
B- 7:10
C- 2:5
D- 5:7
Answer
485.7k+ views
Hint: when the body is in rolling motion on an uneven surface, it has both rotation and translation, there are some cases when body rolls without slipping. The role played by mass in translation is played by moment of inertia in rotation.
Complete step by step answer:Linear kinetic energy of a body of mass, m and moving with linear velocity v, is given by
Rotational kinetic energy of a body having moment of inertia I, and angular velocity is given by
Now a body possessing both translational kinetic energy and rotational kinetic energy is given by,
Now to find the desired ratio,
:( )= --(1)
Moment of inertia of solid sphere is and angular velocity can be written as , putting the value in eq (1) we get,
So, the correct option is (D)
Additional information- The moment of inertia of a uniform square plate of mass m and edge an about one of its diagonals comes out to be
Note:Rotational energy is on account of the motion of the body. Always while finding rotational kinetic energy we use moment of inertia, instead of mass. The moment of inertia plays the same role in rotation as it is played by mass in translation. Also, since we have taken the ratio, the result is dimensionless.
Complete step by step answer:Linear kinetic energy of a body of mass, m and moving with linear velocity v, is given by
Rotational kinetic energy of a body having moment of inertia I, and angular velocity
Now a body possessing both translational kinetic energy and rotational kinetic energy is given by,
Now to find the desired ratio,
Moment of inertia of solid sphere is
So, the correct option is (D)
Additional information- The moment of inertia of a uniform square plate of mass m and edge an about one of its diagonals comes out to be
Note:Rotational energy is on account of the motion of the body. Always while finding rotational kinetic energy we use moment of inertia, instead of mass. The moment of inertia plays the same role in rotation as it is played by mass in translation. Also, since we have taken the ratio, the result is dimensionless.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Trending doubts
State and prove Bernoullis theorem class 11 physics CBSE

What are Quantum numbers Explain the quantum number class 11 chemistry CBSE

Write the differences between monocot plants and dicot class 11 biology CBSE

Who built the Grand Trunk Road AChandragupta Maurya class 11 social science CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

State the laws of reflection of light
