Two satellites of equal masses are orbiting the earth in different radii such that time period of revolutions are T and 2T. What is the ratio of moment of inertia of two satellites about the centre of the earth respectively?

Solution

Let R₁ and R₂be the radii of orbits of satellites having time period T and 2T.

According to Kepler's third law,

T² ∝ R³ $space space space therefore space space space space space space space open parentheses straight R subscript 1 over straight R subscript 2 close parentheses cubed equals open parentheses straight T subscript 1 over straight T subscript 2 close parentheses squared equals open parentheses fraction numerator straight T over denominator 2 straight T end fraction close parentheses squared equals 1 fourth therefore space space space space space space space space open parentheses straight R subscript 1 over straight R subscript 2 close parentheses squared equals open parentheses 1 fourth close parentheses to the power of 2 divided by 3 end exponent equals open parentheses 1 half close parentheses to the power of 4 divided by 3 end exponent$

Ratio of the moment of inertia of first to second satellite is,
$straight I subscript 1 over straight I subscript 2 equals mR subscript 1 squared over mR subscript 2 squared equals open parentheses straight R subscript 1 over straight R subscript 2 close parentheses squared equals open parentheses 1 half close parentheses to the power of 4 divided by 3 end exponent$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

Two satellites of equal masses are orbiting the earth in different radii such that time period of revolutions are T and 2T. What is the ratio of moment of inertia of two satellites about the centre of the earth respectively?

Some More Questions From Units and Measurement Chapter

What is the need of measurement?

Define physical quantity.

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?

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