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 about the water level. What is the length of each side of the cube?

examrobotsa's picture

Submitted by examrobotsa on

Q: 4 (IAS/2002)
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 about the water level. What is the length of each side of the cube?

question_subject: 

Science

question_exam: 

IAS

stats: 

0,6,12,5,6,4,3

keywords: 

{'solid cube': [0, 0, 1, 0], 'cube': [0, 0, 2, 0], 'water level': [0, 0, 2, 2], 'kg mass': [0, 0, 1, 1], 'mass': [0, 0, 2, 3], 'length': [0, 0, 1, 0], 'water': [65, 15, 80, 129], 'cm': [2, 0, 7, 20]}

In this problem, the cube is subjected to the forces of gravity, buoyancy from the water, and an additional mass placed on top of it.

Option 1: If the length of each side of the cube was 12 cm, the volume (and therefore the buoyancy force created when submerged in water) would be too large, and the cube would not get immersed even with the addition of the 0.2 kg mass.

Option 2: With side length 10 cm, the cube`s volume in cubic cm matches the additional weight provided by the mass when converted to weight in water (0.2 kg -> 200 gm -> roughly 200 cm^3). Hence, the cube is just fully immersed with the added weight and floats 2 cm above when the weight is removed - indicating the correctness of the solution.

Option 3 and 4: If the cube side was only 8 cm or 6 cm, the volume (and the buoyancy force) would be too small to keep the cube immersed in water even with the addition of the 0.2 kg mass.

Therefore, the correct answer is option 2: a side length of 10 cm.