Eight practice questions with full answers covering the whole chapter — test yourself before the quiz.
UNITS & MEASUREMENTS — PRACTICE SET (answers at the end)
1. Write the dimensional formula of (a) power (b) pressure (c) gravitational constant $G$.
2. Which is dimensionless: strain, force, work, frequency?
3. Significant figures in: (a) $0.00420$ (b) $6.032$ (c) $3.00\times10^{8}$ ?
4. Kinetic energy $K=\tfrac12 mv^{2}$. If $m$ has $2\%$ error and $v$ has $3\%$ error, find the % error in $K$.
5. Check dimensionally whether $T=2\pi\sqrt{\dfrac{L}{g}}$ (pendulum time period) is correct.
6. Convert $72\ \text{km/h}$ into $\text{m/s}$.
7. A Vernier calliper has $1\ \text{MSD}=1\ \text{mm}$ and $10\ \text{VSD}=9\ \text{MSD}$. Find its least count.
8. Round $3.14159$ to 3 significant figures and $0.004567$ to 2 significant figures.
ANSWERS
1. (a) $[M\,L^{2}\,T^{-3}]$ (b) $[M\,L^{-1}\,T^{-2}]$ (c) $[M^{-1}\,L^{3}\,T^{-2}]$
2. Strain (a ratio of lengths).
3. (a) 3 (b) 4 (c) 3
4. $\dfrac{\Delta K}{K}=\dfrac{\Delta m}{m}+2\dfrac{\Delta v}{v}=2\%+2(3\%)=8\%$.
5. $\sqrt{\dfrac{L}{g}}=\sqrt{\dfrac{[L]}{[L\,T^{-2}]}}=\sqrt{[T^{2}]}=[T]$; $2\pi$ dimensionless ⇒ correct. ✔
6. $72\times\dfrac{1000}{3600}=20\ \text{m/s}$.
7. $1\ \text{VSD}=0.9\ \text{mm}\Rightarrow \text{LC}=1-0.9=0.1\ \text{mm}$.
8. $3.14$ ; $0.0046$.