SATHEE: Rotational Motion Question 53

Rotational Motion Question 53

Question: The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is:

[AIPMT (S) 2004]

Options:

A) 2 : 3

B) 2 : 1

C) $\sqrt{5} : \sqrt{6}$

D) $1 : \sqrt{2}$

Show Answer

Answer:

Correct Answer: C

Solution:

Key Idea: If a body has mass M and radius of gyration is K, then $I = M K^{2}$ . Moment of inertia of a disc and circular ring about a tangential axis in their planes are respectively.

$I_{d} = \frac{5}{4} M_{d} R^{2}$ $I_{r} = \frac{3}{2} M_{r} R^{2}$

but $I = M K^{2}$

$\Rightarrow$ $K = \sqrt{\frac{1}{M}}$

$\frac{K_{d}}{K_{r}} = \sqrt{\frac{I_{d}}{I_{r}} \times \frac{M_{r}}{M_{d}}}$

or $\frac{I_{d}}{I_{r}} \sqrt{\frac{(5 / 4) M_{d} R^{2}}{(3 / 2) M_{r} R^{2}} \times \frac{M_{r}}{M_{d}}} = \sqrt{\frac{5}{6}}$

$∴$ $I_{d} : I_{r} = \sqrt{5} : \sqrt{6}$

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 53

Question: The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring 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