Question

Conversion of 1 MW power on a new system having basic units of mass, length and time as 10kg, 1dm and 1 minute respectively is

• A. $2.16 \times 10^{12}unit$
• B. $1.26 \times 10^{12}unit$
• C. $2.16 \times 10^{10}unit$
• D. $2 \times 10^{14}unit$

Answer 1

Answer: (A)

$2.16 \times 10^{12}unit$

Answer 2

$\lbrack P\rbrack = \lbrack ML^{2}T^{- 3}\rbrack$

Using the relation $n_{2} = n_{1}\left\lbrack \frac{M_{1}}{M_{2}} \right\rbrack^{x}\left\lbrack \frac{L_{1}}{L_{2}} \right\rbrack^{y}\left\lbrack \frac{T_{1}}{T_{2}} \right\rbrack^{z}$

$= 1 \times 10^{6}\left\lbrack \frac{1kg}{10kg} \right\rbrack^{1}\left\lbrack \frac{1m}{1dm} \right\rbrack^{2}\left\lbrack \frac{1s}{1\min}\lbrack\rbrack^{- 3} \right\rbrack$

[As $1MW = 10^{6}W$]

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