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Units And Measurement

Question
CBSEENPH11019888
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The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named AlphaCentauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun ?

Solution
Distance space of space the space star space from space the space solar space system space equals space 4.29 space ly 1 space light space year space equals space Speed space of space light space cross times space 1 space year space space space space space space space space space space space space space space space space space space space space space equals space 3 space cross times space 10 to the power of 8 space cross times space 365 space cross times space 24 space cross times space 60 space cross times space 60 space space space space space space space space space space space space space space space space space space space space space equals space 94608 space cross times space 10 to the power of 11 space straight m space therefore space 4.29 space ly space equals space 405868.32 space cross times space 10 to the power of 11 space straight m space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket space 1 space parsec space equals space 3.08 cross times 10 to the power of 16 space straight m right square bracket space therefore space 4.29 space ly space equals fraction numerator 405868.32 space cross times space 10 to the power of 11 space straight m over denominator space 3.08 cross times 10 to the power of 16 space straight m end fraction space equals space 1.32 space parsec Now comma space using space the space formula comma space straight theta space equals space straight d over straight D space where comma space straight d space equals space diameter space of space Earth apostrophe straight s space orbit space equals space 3 cross times 10 to the power of 11 space straight m straight D space equals space Distance space of space star space from space the space Earth space equals 405868.32 space cross times space 10 to the power of 11 space end exponent straight m therefore space straight theta space equals space fraction numerator 3 cross times 10 to the power of 11 space straight m over denominator 405868.32 space cross times space 10 to the power of 11 space end exponent straight m end fraction space space space space space space space space equals space 7.39 space cross times space 10 to the power of negative 6 space end exponent rad space But comma space 1 space sec space equals space 4.85 space cross times space 10 to the power of – 6 end exponent space rad therefore space space 7.39 space cross times space 10 to the power of negative 6 space end exponent rad space space equals space fraction numerator 7.39 space cross times space 10 to the power of negative 6 space end exponent over denominator space 4.85 space cross times space 10 to the power of – 6 end exponent space end fraction space equals space 1.52 space "

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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