The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is: (a) 2.2 g/cm³ (b) 2.0 g/cm³ (c) 1.7 g/cm³ (d) 2.5 g/cm³

Answer: (b). LC = 1 MSD - 1 VSD = 1 - 0.9 = 0.1 mm = 0.01 cm D = 2 + 2× 0.01 = 2.02 cm, r = 1.01 cm V = 4/3π(1.01)³ ≈ 4.316 cm³ ρ = (8.635)/(4.316) ≈ 2.0 g/cm³, answer (b).

The diameter of a sphere is measured using a vernier caliper whose 9… | JEE Main 2024 (8 Apr, Shift 1)

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Least Count, Vernier Callipers & Screw Gauge

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1\text{ mm}$ . The main scale reading is $2\text{ cm}$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $g$ , the density of the sphere is:

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Answer: (b)

LC $= 1\text{ MSD} - 1\text{ VSD} = 1 - 0.9 = 0.1$ mm $= 0.01$ cm
$D = 2 + 2\times 0.01 = 2.02$ cm, $r = 1.01$ cm
$V = \tfrac{4}{3}\pi(1.01)^3 \approx 4.316\text{ cm}^3$
$\rho = \dfrac{8.635}{4.316} \approx 2.0\text{ g/cm}^3$ , answer (b).

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