UPSC Prelims 2002 · General Studies
Question 4: Science and Technology
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?
AnswerThe answer is (b).
Let the side be a cm. Without the mass the cube floats with 2 cm out of the water, so it displaces a-squared x (a - 2) cm3. With the 0.2 kg (200 g) on top it is just fully immersed, displacing a-squared x a. The extra water displaced weighs 200 g, and water is 1 g/cm3, so a-squared x 2 = 200. Hence a-squared = 100 and a = 10 cm.
Why each option is right or wrong
- (a) 12 cm would need 288 g (2 x 144) of load, not 200 g.
- (b) Right: 2a-squared = 200 gives a = 10 cm.
- (c) 8 cm would need only 128 g (2 x 64).
- (d) 6 cm would need only 72 g (2 x 36).
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2002, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.