# In a certain system, $1$ unit of time is $5\;sec,$ 1 unit of mass is $20 \;kg$ and 1 unit of length is $10 m$. In this system $1$ unit of power corresponds to

$(a)\;16\;watts\quad (b)\;\frac{1}{16} watts\quad (c)\;25 \;watts \quad (d)\;none\;of\;these$

$1 sec ^*=5 \; seconds$
$1 kg ^*=20 \;kg$
$1 m ^*=10 \; m$
$1 watt ^*=1 kg\;m^2 \; sec^{-3}$
$\quad\qquad=\large\frac{1}{20} $$kg^{*}\bigg(\large\frac{1}{10}$$m^ *\bigg)^2\bigg(\large\frac{1}{5} $$\sec ^*\bigg)^{-3} \qquad\quad=\large\frac{1}{20} \times \frac{1}{100}$$\times 125 \;kg ^*\;m^{\large*^2} \;sec ^{\large*^{-3}}$
$\qquad\quad=\large\frac{1}{16} $$watt^* Hence 1 unit of power=\large\frac{1}{16}$$ watts$
Hence b is the correct answer.

edited Jan 9, 2014 by meena.p