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Q27 (NDA-I/2008) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

Consider the following statements: The fraction of a ball floating inside the liquid depends upon 1. density of the liquid 2. mass of the ball 3. density of the ball Which of the statements given above are correct?

Result
Your answer: —  ·  Correct: C
Explanation

According to Archimedes' Principle, an object floats when the buoyant force equals its weight [1]. For a floating object, the fraction of the volume submerged (fraction inside the liquid) is mathematically expressed as the ratio of the density of the object to the density of the fluid (V_submerged / V_total = ρ_object / ρ_fluid) [t1][t6]. This relationship demonstrates that the submerged fraction depends solely on the relative densities of the ball and the liquid [t3][t5]. While the mass of the ball determines its total weight, it does not independently affect the fraction submerged because any change in mass (for a fixed density) results in a proportional change in total volume, keeping the ratio constant [c3][t4]. Therefore, only the density of the liquid and the density of the ball determine the fraction floating inside the liquid.

Sources

  1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > A step further > p. 76
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