Question

In a new system of units, unit of mass is $10kg$, unit of length is $1km$ and unit of time is $1minute$. The value of $1joule$ in this new hypothetical system is :

• A. $3.6\times {10}^{-4}$ new units
• B. $6\times {10}^7$ new units
• C. ${10}^{11}$ new units
• D. $1.67\times {10}^4$ new units

Answer 1

Answer: (A)

Units of Joule are $M{L}^2{T}^{-2}=kg{m}^2{s}^{-2}$

$n_2=n_1\left[\frac{M_1}{M_2}\right]{\left[\frac{L_1}{L_2}\right]}^2{\left[\frac{T_1}{T_2}\right]}^{-2}$

$=1\left[\frac{1kg}{10kg}\right]{\left[\frac{1m}{1km}\right]}^2{\left[\frac{1s}{1min}\right]}^{-2}$

$=1\left[\frac{1}{10}\right]{\left[\frac{1}{1000}\right]}^2{\left[\frac{1}{60}\right]}^{-2}=3.6\times {10}^{-4}units$