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Question 1 calorie = 4.2 J , where 1J = 1 Kgm^2 s^{-2} But in a new system unit of mass equals to alpha Kg . The unit of length beta m and the unit of time gamma Sec . Then 1 calorie has a magnitude of A. 4.2 alpha beta ^2gamma ^{-2} B. 4.2 alpha ^{-1}beta ^{-2}gamma ^2 C. 4.2 alpha beta gamma D. 4.2 alpha ^{-1}beta ^{-1}gamma ^{-1} Answer is B, But How ?

Answers (1)

Given that,

1 calorie = 4.2 (1kg) (1m2) (s-2)

New unit of mass = α kg

Hence, in terms of the new unit, 1 kg = 1/a a = a-1

In terms of the new unit of length,

And, in terms of the new unit of time,

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