Verified Solution • 2025–26 Session moderate

Q1.1: UNITS AND MEASUREMENT Solutions — NCERT Physics - Part 1

⚠️ Common Exam Traps & Conceptual Pitfalls

When converting units for derived quantities like volume or density, students often apply the linear conversion factor (e.g., $10^{-2}$ for cm to m) instead of raising it to the power of the dimension (e.g., $(10^{-2})^3 = 10^{-6}$ for volume). Always verify the exponent of the conversion factor matches the power of the unit in the quantity.

Fill in the blanks

(a) The volume of a cube of side 1 cm is equal to .....m_

(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ...(mm)_

(c) A vehicle moving with a speed of 18 km h__ covers....m in 1 s

(d) The relative density of lead is 11.3. Its density is ....g cm__ or ....kg m__

Multiple Choice Options

  • A
  • B
  • C
  • D

Step-by-Step Verified Solution

**Answer:** (a) 10−610^{-6} m_ (b) 1.5×1041.5 \times 10^4 mm_ (c) 5 m (d) 11.3 g cm__, 1.13×1041.13 \times 10^4 kg m__

**Step-by-Step Explanation:**

(a) Volume of cube = (1 cm)3=1 cm3=10−6 m3(1 \text{ cm})^3 = 1 \text{ cm}^3 = 10^{-6} \text{ m}^3.

(b) Surface area of cylinder = 2πr(r+h)=2π(2.0)(2.0+10.0)=150.8 cm2=15080 mm2≈1.5×104 mm22\pi r(r+h) = 2\pi(2.0)(2.0+10.0) = 150.8 \text{ cm}^2 = 15080 \text{ mm}^2 \approx 1.5 \times 10^4 \text{ mm}^2.

(c) Speed = 18 km/h=18×518=5 m/s18 \text{ km/h} = 18 \times \frac{5}{18} = 5 \text{ m/s}. Distance in 1 s = 5 m.

(d) Relative density = 11.3 means density = 11.3 g cm−311.3 \text{ g cm}^{-3}. In SI: 11.3×1000=1.13×104 kg m−311.3 \times 1000 = 1.13 \times 10^4 \text{ kg m}^{-3}.

All Questions in this Chapter

Q1.1 Q1.2 Q1.3 Q1.4 Q1.5 Q1.6 Q1.7 Q1.8 Q1.9 Q1.10 Q1.11 Q1.12 Q1.13 Q1.14 Q1.15 Q1.16 Q1.17

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