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Units And Measurement

Question
CBSEENPH11016582
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A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2 sñ2. Suppose we employ a system of units in which the unit of mass equals αkg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 straight alpha to the power of negative 1 end exponent straight beta to the power of negative 1 end exponent straight gamma squared in terms of the new units. 

Solution
We know that dimensional formula of heat energy is open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 2 end exponent close square brackets
It is given that,
1 cal = 4.2J 
In SI system,   
M1 = 1 kg, L1 = 1 m,  T1 = 1 s 
In new system of units, 
straight M subscript 2 equals straight alpha space kg comma space straight L subscript 2 equals straight beta space straight m comma space straight T subscript 2 equals straight gamma space straight s
We  know,  
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space space space space straight n subscript 2 equals 4.2 open parentheses fraction numerator 1 space kg over denominator straight alpha space kg end fraction close parentheses to the power of 1 open parentheses fraction numerator 1 space straight m over denominator straight beta space straight m end fraction close parentheses squared open parentheses fraction numerator 1 space straight s over denominator straight gamma space straight s end fraction close parentheses to the power of negative 2 end exponent
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therefore space space space space space space space space 1 space cal space equals space equals 4.2 straight alpha to the power of negative 1 end exponent straight beta to the power of negative 2 end exponent straight gamma squared space new space unit 

Some More Questions From Units and Measurement Chapter

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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