Question

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

The dimensional formula of energy is $\left[ ML ^{2} T ^{-2}\right]$.
$n_{2}=1\left[\frac{1 kg }{10 kg }\right]^{1}\left[\frac{1 m }{1 km }\right]^{2}\left[\frac{1 s }{1 min }\right]^{-2}$
$=\frac{1}{10} \times \frac{1}{10^{6}} \times \frac{1}{(60)^{-2}}$
$=\frac{3600}{10^{7}}=3.6 \times 10^{-4}$