The diameter of a sphere is measured using a vernier caliper whose...

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 \mathrm{~mm}

. The main scale reading is

2 \mathrm{~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:

Options

A $2.0 \mathrm{~g} / \mathrm{cm}^3$
B $1.7 \mathrm{~g} / \mathrm{cm}^3$
C $2.2 \mathrm{~g} / \mathrm{cm}^3$
D $2.5 \mathrm{~g} / \mathrm{cm}^3$

Correct answer

A. $2.0 \mathrm{~g} / \mathrm{cm}^3$

Step-by-step solution

Given

9 \mathrm{MSD}=10 \mathrm{VSD} \operatorname{mass}=8.635 \mathrm{~g}

\begin{aligned} & \mathrm{LC}=1 \mathrm{MSD}-1 \mathrm{VSD} \\ & \mathrm{LC}=1 \mathrm{MSD}-\frac{9}{10} \mathrm{MSD} \\ & \mathrm{LC}=\frac{1}{10} \mathrm{MSD} \\ & \mathrm{LC}=0.01 \mathrm{~cm}\end{aligned}

Reading of diameter $=\mathrm{MSR}+\mathrm{LC} \times \mathrm{VSR}

\begin{aligned} & =2 \mathrm{~cm}+(0.01) \times(2) \\ & =2.02 \mathrm{~cm}\end{aligned}$$

Volume of sphere

=\frac{4}{3} \pi\left(\frac{d}{2}\right)^3=\frac{4}{3} \pi\left(\frac{2.02}{2}\right)^3 =4.32 \mathrm{~cm}^3

Density

=\frac{\text{ mass }}{\text{ volume }}=\frac{8.635}{4.32}=1.998 \sim 2.00 \mathrm{~g}$

Practice Experimental Physics on Quantrex Academy →

More from Experimental Physics

Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter d are given.… JEE Advanced 2026 In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is… JEE Main 2026 In a screw gauge when the circular scale is given five complete rotations it moves… JEE Main 2026 In a screw gauge the zero of main scale reference line coincides with the fifth division… JEE Main 2026 In an experiment, a set of reading are obtained as follows - 1.24 ~mm, 1.25 ~mm, 1.23 ~mm… JEE Main 2026 When both jaws of vernier callipers touch each other, zero mark of the vernier scale is… JEE Main 2026 In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions.… JEE Main 2026 In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal… JEE Main 2026 Full Experimental Physics list All JEE Main PYQs