UPSC Prelims 2002 Q4: Science & Technology – Physics
A solid cube just gets completely immersed in water when a 0.2 kg mass is placed on it. If the
mass is removed, the cube is 2 cm above the water level. What is the length of each side of the
cube?
- (a) 12 cm
- (b) 10 cm
- (c) 8 cm
- (d) 6 cm
Answer: (b) 10 cm
Explanation
Side of a cube from the water displaced by a 0.2 kg mass
| Step | Working |
|---|---|
| Floating condition | Without the mass the cube floats with 2 cm of its height above water |
| Extra load needed to sink it | The 0.2 kg (200 g) mass pushes down exactly that 2 cm layer into the water |
| Archimedes' principle | Weight of the added mass = weight of extra water displaced: 200 g = s² × 2 cm × 1 g/cm³ |
| Solve | s² = 100 cm², so s = 10 cm |
A solid cube is just completely immersed in water when the 0.2 kg mass is placed on it, so the length of each side of the cube follows from the displaced water. The extra volume of water displaced is the base area s² times the 2 cm layer. Since 1 cm³ of water has a mass of 1 g, 200 g of water has a volume of 200 cm³. So 2s² = 200, which gives s² = 100 and the side of the cube is 10 cm.
Answer: (b) 10 cm.
Why each option is right or wrong
- (a) Incorrect. A 12 cm side would need a mass of 288 g.
- (b) CORRECT. 2 × 10 × 10 = 200 cm³ of water = 200 g.
- (c) Incorrect. An 8 cm side would need only 128 g.
- (d) Incorrect. A 6 cm side would need only 72 g.
Key point
A floating body displaces water equal to its weight; an extra load displaces extra water equal to the load.
Remember
Added load 200 g = side² × 2 cm × 1 g/cm³, so the side is 10 cm.
Common mistakes
- Forgetting that the 2 cm is the height above water, not a side length.
- Using volume 2 × s instead of s² × 2.
- Mixing kg and g and getting a side of 0.2 or 20 cm.
Exam tip
Test each option: extra water = 2 × side² must equal 200.
Sources
- NCERT Class IX Science — Gravitation (Archimedes' principle)
- NCERT Class XI Physics — Mechanical Properties of Fluids (Archimedes' principle)