The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is  from Physics System of Particles and Rotational Motion Class 11 Manipur Board
Zigya Logo

Chapter Chosen

System of Particles and Rotational Motion

Book Chosen

Physics Part I

Subject Chosen

Physics

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is 

  • square root of 3 colon square root of 2
  • 1 colon square root of 2
  • square root of 2 colon 1
  • square root of 2 colon space square root of 3

B.

1 colon square root of 2

The square root of the ratio of the moment of inertia of rigid body nad its mass is called radius of gyration.
As in key idea, radius of gyration is given by
straight K space equals space square root of straight I over straight M end root
For space given space problem
straight K subscript disc over straight K subscript ring space equals space square root of straight I subscript disc over straight I subscript ring end root
But space straight I subscript disc space left parenthesis about space its space axis right parenthesis space equals space 1 half MR squared
and space straight I subscript ring space left parenthesis about space its space axis right parenthesis space equals MR squared
Where space straight R space is space the space the space radius space of space both space bodies.
Therefore comma space eq left parenthesis straight i right parenthesis space becomes
straight K straight K subscript disc over straight K subscript ring space equals space square root of fraction numerator begin display style 1 half end style MR squared over denominator MR squared end fraction end root space equals space 1 colon square root of 2

The square root of the ratio of the moment of inertia of rigid body nad its mass is called radius of gyration.
As in key idea, radius of gyration is given by
straight K space equals space square root of straight I over straight M end root
For space given space problem
straight K subscript disc over straight K subscript ring space equals space square root of straight I subscript disc over straight I subscript ring end root
But space straight I subscript disc space left parenthesis about space its space axis right parenthesis space equals space 1 half MR squared
and space straight I subscript ring space left parenthesis about space its space axis right parenthesis space equals MR squared
Where space straight R space is space the space the space radius space of space both space bodies.
Therefore comma space eq left parenthesis straight i right parenthesis space becomes
straight K straight K subscript disc over straight K subscript ring space equals space square root of fraction numerator begin display style 1 half end style MR squared over denominator MR squared end fraction end root space equals space 1 colon square root of 2

916 Views

What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system. 
794 Views

Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion. 
943 Views

What is the need of centre of mass?

Newton’s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object. 
911 Views

Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated. 
1449 Views

Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.
730 Views