If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?
Answer
Yes, No $[\omega = 2\pi\text{f}]$$\omega$ has unit rad/ sec but frequency has hertz.
The normal duration of I.Sc. Physics practical period in Indian colleges is 100 minutes. Express this period in microcenturies. 1 microcentury $= 10^{-6} × 100$ years. How many microcenturies did you sleep yesterday?
Answer
1 micro century $=10^4 \times 100$ years $=10^{-4} \times 365 \times 24 \times 60 \mathrm{~min}$
So, $100\text{ min}=\frac{10^5}{52560}=1.9\text{ microcentury}$