Question

Calorie is a unit of heat or energy whose value is $4.2J$, where $J=1kg{m}^2{s}^{-2}$. If one uses a unit system in which units of mass, length and time are taken as $\alpha kg,\beta metre$ and $\gamma second$ respectively, then the value of calorie in this system will be

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

Answer 1

Answer: (A)

$4.2{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$

$\because 1cal=4.2J\therefore 1cal=4.2kg{m}^2{s}^{-2}$

$=\left(4.2{\alpha }^{-1}{\beta }^{-2}{\gamma }^2\right)\left(\alpha kg\right)\left(\beta m{)}^2\right(\gamma s{)}^{-2}$