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JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Fluid Mechanics

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A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?
  1. (A)(see graph)
  2. (B)(see graph)
    ✓ Correct
  3. (C)(see graph)
  4. (D)(see graph)

Answer: (B)

Solution

As the steel ball falls through glycerine, the net downward force is

where is buoyancy and the last term is the viscous (Stokes) drag. Solving this linear equation gives

for positive constants . The velocity rises from zero and asymptotically approaches a constant terminal velocity, with continuously decreasing slope and no overshoot — the curve showing this saturating rise is option (2).

JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Single correct option

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