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 $kg{m}^2{s}^{-2}$.
The magnitude of calorie in $SI$ unit is $4.2kg{m}^2{s}^2$
we have
$(n_1{v}_1)=(n_2{u}_2)$
$4.2kg{m}^2{s}^{-2}=\alpha {\beta }^2{\gamma }^{2}kg{m}^2{s}^{-2}$
$n_2=4.2{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$