Question
In a certain system of units, $$1$$ unit of time is $$5\,\sec,$$ $$1$$ unit of mass is $$20\,kg$$ and $$1$$ unit of length is $$10\,m.$$ In this system, one unit of power will correspond to-
A.
$$16\,watts$$
B.
$$\frac{1}{{16}}\,watts$$
C.
$$25\,watts$$
D.
$$\frac{1}{{25}}\,watts$$
Answer :
$$\frac{1}{{16}}\,watts$$
Solution :
$$\eqalign{
& 1\,{\sec ^ * } = 5\,\sec ,1k{g^ * } = 20\,kg,1\,{m^ * } = 10\,m \cr
& 1\,watt = 1\,kg\,{m^2}{\sec ^{ - 3}} \cr
& = \frac{1}{{20}}k{g^ * }{\left( {\frac{1}{{10}}{m^ * }} \right)^2}{\left( {\frac{1}{5}{{\sec }^ * }} \right)^{ - 3}} \cr
& = \frac{1}{{20}} \times \frac{1}{{100}} \times 125\,k{g^ * }{m^{ * 2}}{\sec ^{ * - 3}} = \frac{1}{{16}}wat{t^ * } \cr} $$