Question

In a new system the unit of mass is $\alpha\, kg$, unit of length is $\beta m$ and unit of times of $\gamma s$. The value of $1\, J$ in this new system is :-

• A. $\frac{\gamma^{2}}{\alpha \beta^{2}}$
• B. $\frac{\gamma \alpha}{\beta^{2}}$
• C. $\alpha \beta \gamma$
• D. $\alpha \gamma^{2} / \beta^{2}$

Answer 1

Answer: (A)

$n _{2}= n _{1}$
$\left[\frac{ M _{1}}{ M _{2}}\right]^{1}\left[\frac{ L _{1}}{ L _{2}}\right]^{2}\left[\frac{ T _{1}}{ T _{2}}\right]^{-2} $
$=1 \times \frac{1}{\alpha} \times\left(\frac{1}{\beta}\right)^{2} \times\left(\frac{1}{\gamma}\right)^{-2}$
$=\gamma^{2} / \alpha \beta^{2}$