floating-sinking-and-density MCQs for UPSC Prelims

30 practice questions on floating-sinking-and-density from the The Amazing World of Solutes, Solvents, and Solutions section of the UPSC Prelims syllabus. 30 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

9 Easy 15 Medium 6 Hard

Sample questions

Q1
easy

A block has a mass of $60\ \text{g}$ and a volume of $30\ \text{cm}^3$. Its density is

  1. A $1800\ \text{g/cm}^3$
  2. B $0.5\ \text{g/cm}^3$
  3. C $2\ \text{g/cm}^3$
  4. D $30\ \text{g/cm}^3$
Show answer and explanation

Correct answer: C - $2\ \text{g/cm}^3$

Density is mass divided by volume, so it is $60 \div 30 = 2\ \text{g/cm}^3$. Dividing the volume by the mass gives $0.5$, which is the common reversal slip. The value $30$ is just the volume copied down, and $1800$ comes from multiplying instead of dividing.

Q2
medium

Equal volumes of milk and honey are taken in two identical cups and weighed. The cup of honey is found to be heavier. It follows that

  1. A the two have equal densities
  2. B honey is denser than milk
  3. C milk is denser than honey
  4. D honey occupies a larger volume than milk
Show answer and explanation

Correct answer: B - honey is denser than milk

For equal volumes, the heavier sample has more mass in the same space, so honey is denser. The second option reverses this and the third contradicts the weighing. The volumes were made equal at the start, so honey cannot occupy more space.

Q3
medium

A solid cube of side $2\ \text{cm}$ has a mass of $32\ \text{g}$. The density of the material of the cube is

  1. A $64\ \text{g/cm}^3$
  2. B $4\ \text{g/cm}^3$
  3. C $8\ \text{g/cm}^3$
  4. D $16\ \text{g/cm}^3$
Show answer and explanation

Correct answer: B - $4\ \text{g/cm}^3$

The volume of the cube is $2 \times 2 \times 2 = 8\ \text{cm}^3$, so the density is $32 \div 8 = 4\ \text{g/cm}^3$. The value $8$ is the volume itself, and $16$ comes from dividing the mass by the side instead of the volume. Multiplying mass by the side gives $64$, which is not a density.

Q4
hard

A metal piece of mass $54\ \text{g}$ is lowered into a measuring cylinder holding water, and the water level rises from $50\ \text{mL}$ to $70\ \text{mL}$. The density of the metal is

  1. A $2.7\ \text{g/cm}^3$
  2. B $0.37\ \text{g/cm}^3$
  3. C $0.77\ \text{g/cm}^3$
  4. D $1.08\ \text{g/cm}^3$
Show answer and explanation

Correct answer: A - $2.7\ \text{g/cm}^3$

The metal pushes aside water equal to its own volume, so its volume is $70 - 50 = 20\ \text{cm}^3$ and its density is $54 \div 20 = 2.7\ \text{g/cm}^3$. Using $50$ or $70$ as the volume gives $1.08$ and $0.77$, both of which ignore the rise in level. The value $0.37$ divides the volume by the mass.

Q5
medium

Cooking oil poured into a bowl of water settles as a separate layer above the water. This tells us that the oil is

  1. A less dense than water
  2. B exactly as dense as water
  3. C denser than water
  4. D without any density
Show answer and explanation

Correct answer: A - less dense than water

Of two liquids that do not mix, the less dense one rests on top, so the oil must be less dense than water. If it were denser it would sink below the water, and equal densities would let it stay mixed rather than form a clear upper layer. Every substance has a density.

Q6
hard

Four cubes of the same size are placed in water. Cube P floats with most of it above the surface, cube Q floats with only a little above, cube R stays wherever it is placed inside the water without rising or sinking, and cube S sinks to the bottom. Arranged from least dense to most dense, the cubes are

  1. A S, R, Q, P
  2. B P, Q, R, S
  3. C R, P, Q, S
  4. D Q, P, S, R
Show answer and explanation

Correct answer: B - P, Q, R, S

The more of a cube that stays above the surface, the less dense it is, so P is lighter for its size than Q. Cube R neither rises nor sinks, so its density matches that of water, and S sinks, so it is denser than water. That gives the order P, Q, R, S, and the other sequences break this pattern.

Q7
medium

Consider these statements. Statement I: A substance that floats on water has a density less than that of water. Statement II: An iron nail sinks in water because iron is less dense than water.

  1. A Both statements are correct
  2. B Only Statement II is correct
  3. C Both statements are wrong
  4. D Only Statement I is correct
Show answer and explanation

Correct answer: D - Only Statement I is correct

Floating means the substance is less dense than the liquid, so Statement I is correct. A nail sinks because iron is denser than water, so Statement II gives the right result with the wrong reason and is wrong as written. Only the first statement holds.

Q8
medium

Two blocks have exactly the same mass, but block P takes up a larger volume than block Q. The denser block is

  1. A Q
  2. B P
  3. C impossible to identify even in principle
  4. D neither, since their masses are equal
Show answer and explanation

Correct answer: A - Q

The same mass squeezed into a smaller volume means more matter per unit space, so Q is denser. P spreads the same mass over more space and is therefore less dense. Equal masses do not mean equal densities unless the volumes match too, and the comparison here is quite possible.

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