SATHEE: Rotational Motion Question 194

Rotational Motion Question 194

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:

A) $1 : \sqrt{2}$

B) l : 3

C) 2: l

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

Show Answer

Answer:

Correct Answer: D

Solution:

[d]

$I_{y_{1}} = \frac{M R^{2}}{4}$

$∴ I^{'} y_{1} = \frac{M R^{2}}{4} + M R^{2} = \frac{5}{4} M R^{2} .$

$I_{y_{2}} = \frac{M R^{2}}{2}$

$∴ I_{y_{2}}^{'} = \frac{M R^{2}}{2} + M R^{2} = \frac{3}{2} M R^{2}$

$I^{'} y_{1} = M K_{1}^{2}, I^{'} y_{2} = M K_{2}^{2}$

$∴ \frac{K_{1}^{2}}{K_{2}^{2}} = \frac{I_{y_{1}}^{'}}{I^{'} y_{2}} \Rightarrow K_{1} : K_{2} = \sqrt{5} : \sqrt{6}$

Rotational Motion Question 194

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

Rotational Motion Question 194

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

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