Q. In a new system of units, unit $f$ mass is 10 kg, unit of length is 1 km and unit of time is 1 min. The value of 1 joule in this new hypothertical 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
Explanation
We know that the dimensional formula of energy is $\lbrack ML^{2}T^{- 2}\rbrack$ $n_{2} = 1\lbrack\left\lbrack \frac{1kg}{10kg} \right\rbrack^{1}\left\lbrack \frac{1m}{1km} \right\rbrack\left\lbrack \frac{1s}{1\ min} \right\rbrack^{2}$ $= \frac{1}{10} \times \frac{1}{10^{6}} \times \frac{1}{(60)^{- 2}} = \frac{3600}{10^{7}} = 3.6 \times 10^{- 4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.