Question

If $\alpha \text{kilogram}$, $\beta \text{meter}$, and $\gamma \text{second}$ are the fundamental units, $1\text{cal}$ can be expressed in new units as $[1\text{cal}=4.2\text{J}]$

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

Answer 1

The correct option is D $4.2{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$

We have,
$1cal=4.2J$
$1cal=4.2\frac{kg-m^2}{s^2}$

From the given fundamental units, we can write:
$1kg=\frac{1}{\alpha }$
$1m=\frac{1}{\beta }$
$1s=\frac{1}{\gamma }$

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