Paper II · Part B — Physics

Density, Specific Gravity and Archimedes' Principle

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Concept

Density is mass per unit volume; specific gravity (relative density) compares a substance's density with that of water. Archimedes' principle explains buoyancy — why objects float or sink.

An object floats if its density is less than that of the fluid.

Key Points & Formulas

Density = mass / volume.
Specific gravity = density of substance / density of water (no unit).
Archimedes: upthrust = weight of fluid displaced.
Floats if density < fluid density; sinks if greater.

Worked Example

Q. A block of 200 g occupies 250 cm³. Find its density and state whether it floats in water.

Density = 200/250 = 0.8 g/cm³.

Water's density is 1 g/cm³; 0.8 < 1, so the block floats.

Common traps

Reading the prompt too quickly and missing a qualifier.
Memorising the result without checking when it applies.
Skipping units, signs, chronology or the final reasonableness check.

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State the governing rule before substituting values.
Eliminate impossible options before doing full calculation.

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5 NDA questions

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Question 1

NDA Practice 2026

The instrument used to measure atmospheric pressure is the

Question 2

NDA II 2025

A body sinks in water when

Question 3

NDA II 2024

A pumpkin weighs 7.5 N. On submerging it completely in water, 3/4 L of water gets displaced. The acceleration due to gravity at the place where the pumpkin was weighed is 10 m/s². Which one of the following is the correct value of the density of the pumpkin ?

Question 4

NDA II 2024

Shown in the figure are two hollow cubes C₁ and C₂ of negligible mass partially filled with liquids of densities ρ₁ and ρ₂ respectively, floating in water (density ρw). The relationship between ρ₁, ρ₂ and ρw is
density

Question 5

NDA I 2023

A sphere of volume $V$ is made of a material with lower density than water. While on Earth, it floats on water with its volume $f_1V$ ( $f_1 \lt 1$ ) submerged. On the other hand, on a spaceship accelerating with acceleration $a \lt g$ (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is $f_2V$ . Then:

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