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?

By Archimedes' principle, the buoyant force equals the weight of fluid displaced [1]. Let cube side = s cm. Without the 0.2 kg mass the cube stands 2 cm above water, so submerged depth = s − 2 and displaced volume V1 = s^2(s − 2). With the 0.2 kg (200 g) mass the cube is just fully submerged, so V2 = s^3. The extra displaced volume ΔV = V2 − V1 = 2s^2 must equal the volume of 200 g of water. Using water density ≈ 1 g/cm^3 (1 mL = 1 g) [2], ΔV = 200 cm^3, hence 2s^2 = 200 ⇒ s^2 = 100 ⇒ s = 10 cm. Therefore option 2 is correct.

Sources

1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > A step further > p. 76
2. [2] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 9: The Amazing World of Solutes, Solvents, and Solutions > Conversion factor for density > p. 141