Calculate the radius of gyration of hollow sphere about its diameter and tangent.

Solution

Let M be the mass and R be the radius of hollow sphere.

(i) Radius of gyration about diameter:

Moment of inertia of hollow sphere about diameter is,
$straight I equals 2 over 3 MR squared$
If K_d is radius of gyration about diameter then,
$space space space space space space space space M K subscript straight d squared equals 2 over 3 M R squared rightwards double arrow space space space space space space space straight K subscript straight d equals square root of 2 over 3 end root straight R$

(ii) Radius of gyration about tangent:

Moment of inertia of hollow sphere about tangent can be calculated by using the theorem of parallel axis.
That is,
$straight I subscript 1 equals straight I subscript straight d plus MR squared equals 2 over 3 MR squared plus MR squared equals 5 over 3 MR squared$
If K_t is radius of gyration about tangent then,
$MK subscript straight t squared equals 5 over 3 MR squared space space space space space straight K subscript straight t equals square root of 5 over 3 end root straight R subscript 0$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

Calculate the radius of gyration of hollow sphere about its diameter and tangent.

Some More Questions From Units and Measurement Chapter

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.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

How many fundamental quantities are there in Physics?

Name the fundamental quantities of mechanics.

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