SATHEE: Rotational Motion Question 65

Rotational Motion Question 65

Question: 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

[AIPMPT (S) 2008]

Options:

A) $\sqrt{3} : \sqrt{2}$

B) $1 : \sqrt{2}$

C) $\sqrt{2} : 1$

D) $\sqrt{2} : \sqrt{3}$

Show Answer

Answer:

Correct Answer: B

Solution:

Key Idea: The square root of the ratio of the moment of inertia of a rigid body and its mass is called radius of gyration.

As in key idea, radius of gyration is given by

$K = \sqrt{\frac{I}{M}}$ For given problem

$\frac{K_{d i s c}}{K_{r i n g}} = \sqrt{\frac{I_{d i s c}}{I_{r i n g}}}$

But $I_{d i s c}$ (about its axis) $= \frac{1}{2} M R^{2}$

and $I_{r i n g}$ (about its axis) $= M R^{2}$ where R is the radius of both bodies.

Therefore, Eq.

(i) becomes

$\frac{K_{d i s c}}{K_{r i n g}} = \sqrt{\frac{\frac{1}{2} M R^{2}}{M R^{2}}} = 1 : \sqrt{2}$

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Rotational Motion Question 65

Question: 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

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu