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 of these is dimensionless: strain, force, work, frequency?
3. How many significant figures are in: (a) 0.00420 (b) 6.032 (c) 45000 (d) 3.00 × 10^8 ?
4. A body's kinetic energy is K = ½mv². If m is measured with 2% error and v with 3% error, find the % error in K.
5. Check dimensionally whether T = 2π√(L/g) (time period of a pendulum) is correct.
6. Convert 72 km/h into m/s.
7. A Vernier calliper has 1 MSD = 1 mm and 10 vernier divisions equal to 9 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 (it is a ratio of lengths).
3. (a) 3 (b) 4 (c) 2 (trailing zeros without a decimal are ambiguous — treat as 2) (d) 3
4. ΔK/K = Δm/m + 2(Δv/v) = 2% + 2(3%) = 8%.
5. [√(L/g)] = √([L]/[L T^-2]) = √([T²]) = [T]; 2π is dimensionless → correct. ✔
6. 72 × (1000/3600) = 20 m/s.
7. LC = 1 MSD − 1 VSD = 1 − 0.9 = 0.1 mm (since 10 VSD = 9 MSD → 1 VSD = 0.9 mm).
8. 3.14 ; 0.0046.