Question

If the unit of power is $1$ million erg per minute, the unit of force is $1000$ dyne and that of time is $\frac{1}{10}$s, the unit of mass in the new system is :

• A. 6 g
• B. 60 g
• C. 106 g
• D. 1 g

Answer 1

Answer: (A)

6 g

We have units of power as $\frac{kg{m}^2}{s^3}$
and units of force as $\frac{kgm}{s^2}$
Thus we get the $\frac{Power}{Forc{e}^2}=\frac{s}{kg}$
We have power as ${10}^6$ ergs per min$=\frac{1}{600}Nm/s$
and force as $1000dynes={10}^{-2}N$
Thus we get $\frac{Power}{Forc{e}^2}=\frac{{10}^4}{600}s/kg$
Taking its reciprocal and multiplying it by unit of time we get
$\frac{6}{100}\times \frac{1}{10}=\frac{6}{1000}kg=6g$