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

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

Solution

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
$straight K space equals space square root of straight I over straight M end root For space given space problem straight K subscript disc over straight K subscript ring space equals space square root of straight I subscript disc over straight I subscript ring end root But space straight I subscript disc space left parenthesis about space its space axis right parenthesis space equals space 1 half MR squared and space straight I subscript ring space left parenthesis about space its space axis right parenthesis space equals MR squared Where space straight R space is space the space the space radius space of space both space bodies. Therefore comma space eq left parenthesis straight i right parenthesis space becomes straight K straight K subscript disc over straight K subscript ring space equals space square root of fraction numerator begin display style 1 half end style MR squared over denominator MR squared end fraction end root space equals space 1 colon square root of 2$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

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

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

Some More Questions From Units and Measurement Chapter

Give four examples of physical quantities.

Define unit.

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

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