Question

If mass is measure in units of $ \alpha \,kg $ , length in $ \beta\, m $ and time in $ \gamma $ s then calorie would be

• A. $ 4.2\alpha\beta^{2}\gamma^{-2} $
• B. $ 4.2\alpha^{-1}\beta^{2}\gamma^{2} $
• C. $ 4.2\alpha^{-1}\beta^{-2}\gamma^{2} $
• D. $ 4.2\alpha^{-2}\beta^{-1}\gamma^{-2} $

Answer 1

Answer: (C)

The $SI$ system, the unit of heat is $J$ or $kg \,m^2s^{-2}$.
The magnitude of calorie in $SI$ unit is $4.2 \,kg \,m^2 \,s^2$
we have
$(n_1v_1) = (n_2u_2)$
$ 4.2 \,kgm^2s^{-2} = \alpha \beta^2 \gamma^2 \,kgm^2s^{-2}$
$n_2 = 4.2 \,\alpha^{-1}\beta^{-2} \gamma^2$