Question

1 Joule of energy is to be converted into a new system of units in which length is measured in 10 meters, mass in 10Kg and time in 1 minute. What is the numerical value of 1 J in the new system?
A. $ 36\times {{10}^{4}} $
B. $ 36\times {{10}^{-3}} $
C. $ 36\times {{10}^{-2}} $
D. $ 36\times {{10}^{-1}} $

Answer 1

Hint: Change of units is the transformation between various units of estimation for a similar amount, ordinarily through multiplicative change factors. A transformation factor is utilized to change the units of a deliberate amount without changing its worth. The solidarity section strategy for unit change comprises a division wherein the denominator is equivalent to the numerator, yet they are in various units. In view of the character property of duplication, the estimation of an amount won't change as long as it is increased by one. Likewise, if the numerator and denominator of a portion are equivalent to one another, at that point the part is equivalent to one. So as long as the numerator and denominator of the division are the same, they won't influence the estimation of the deliberate amount.
In SI System, the value of 1 J is given by
 $ 1J=1Nm=1Kg{{m}^{2}}/{{s}^{2}} $

Complete step by step solution
Here the new system has 10Kg, 10m and 1min
As 1 min = 60 sec
 $ 1\sec =\dfrac{1}{60}\min $
Also $ 1J=1Kg{{m}^{2}}/{{s}^{2}} $
So value of 1 J in new system is given as
 $ \begin{align}
  & 1J=\left( \dfrac{1}{10} \right)Kg\times {{\left( \dfrac{1}{10} \right)}^{2}}{{m}^{2}}\times {{\left( \dfrac{1}{60} \right)}^{-2}}{{\min }^{-2}} \\
 & =\left( \dfrac{1}{10} \right)Kg\times \left( \dfrac{1}{100} \right){{m}^{2}}\times {{\left( 60 \right)}^{2}}{{\min }^{-2}} \\
 & =3600\times {{10}^{-3}}Kg\ {{m}^{2}}{{\min }^{-2}} \\
 & =36\times {{10}^{-1}}Kg\text{ }{{m}^{2}}{{\min }^{-2}} \\
\end{align} $
Therefore, option (D) is the correct answer.

Note
Remember to put the powers on the modified new system as it is as were in the SI system of units. Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams)