Question

Conversion of $1$ MW power in a system of units having basic units of mass, length and time as $10$ kg, $1$ deci metre and $1$ minute respectively is :

• A. $2.16$ x ${10}^{10}$ unit
• B. $2$ x ${10}^4$ unit
• C. $2.16$ x ${10}^{12}$ unit
• D. $1.26$ x ${10}^{12}$ unit

Answer 1

Answer: (C)

$2.16$ x ${10}^{12}$ unit

$\left[P\right]=\left[M{L}^2{T}^{-3}\right]$

Using the relation $n_2=n_1{\left[\frac{M_1}{M_2}\right]}^x{\left[\frac{L_1}{L_2}\right]}^y{\left[\frac{T_1}{T_2}\right]}^z=1\times {10}^6{\left[\frac{1kg}{10kg}\right]}^1{\left[\frac{1m}{1dm}\right]}^2{\left[\frac{1s}{1min}\right]}^{-3}$

$={10}^6\left[\frac{1kg}{10kg}\right]{\left[\frac{10dm}{1dm}\right]}^2{\left[\frac{1sec}{60sec}\right]}^{-3}=2.16\times {10}^{12}unit$