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How terminal velocity changes with the radius of the drop or ball (v proportional to r squared)

This type of question, asked 7 times: 25 Jun 2022, 11 Apr 2023, 31 Jan 2024, 8 Apr 2024, 21 Jan 2026 S2, 24 Jan 2026 S1, 8 Apr 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    25 Jun 2022

    6
    The terminal velocity (vt)\left( v_{t} \right) of the spherical rain drop depends on the radius (r) of the spherical rain drop as: -

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  2. Question 2

    11 Apr 2023

    91
    Eight equal drops of water are falling through air with a steady speed of 10 cm/s10\text{ }cm/s. If the drops coalesce, the new velocity is: -

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  3. Question 3

    31 Jan 2024

    107
    A small spherical ball of radius rr, falling through a viscous medium of negligible density has terminal velocity 'v'. Another ball of the same mass but of radius 2r2r, falling through the same viscous medium will have terminal velocity:

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  4. Question 4

    8 Apr 2024

    112
    Small water droplets of radius 0.01 mm0.01\text{ }mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s10\text{ }cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _____ cm/scm/s.

  5. Question 5

    21 Jan 2026 S2

    22
    The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s20\text{ }cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ____\_\_\_\_ cm/scm/s.

  6. Question 6

    24 Jan 2026 S1

    25
    Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s10\text{ }cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is ____\_\_\_\_ cm/scm/s.

  7. Question 7

    8 Apr 2026 S2

    9
    A spherical liquid drop of radius R acquires the terminal velocity v1v_{1} when falls through a gas of viscosity η\eta. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity v2v_{2} falling through the same gas. The ratio of terminal velocities v1/v2v_{1}/v_{2} is ____\_\_\_\_ .

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