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Terminal velocity varies as the square of the radius: spheres or raindrops of different size

This type of question, asked 6 times: 3 May 2023 S2, 11 May 2023 S2, 12 May 2024 S2, 20 Apr 2025 S2, 13 May 2026 S1, 14 May 2026 S1. All 6 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    28
    A steel ball of radius 6 mm has a terminal speed of 12 cm s−112\text{ cm s}^{-1} in a viscous liquid. What will be the terminal speed of a steel ball of radius 3 mm in the same liquid?

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  2. Question 2

    11 May 2023 S2

    35
    A lead sphere of mass 'm' falls in viscous liquid with terminal velocity V0V_0. Another lead sphere of mass '8m' but of same material will fall through the same liquid with terminal velocity

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  3. Question 3

    12 May 2024 S2

    5
    A spherical metal ball of radius rr falls through a viscous liquid with terminal velocity VV. Another metal ball of the same material but of radius r3\frac{r}{3} falls through the same liquid. Its terminal velocity will be

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  4. Question 4

    20 Apr 2025 S2

    1
    Two raindrops reach the earth with different terminal velocities having the ratio 9:4. The ratio of their volumes is

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  5. Question 5

    13 May 2026 S1

    111
    Two solid spheres of same material but of mass M and 8M fall simultaneously on a viscous liquid and their terminal velocities are V and nV, then the value of n is

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  6. Question 6

    14 May 2026 S1

    110
    Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16:916 : 9. The ratio of their surface area is

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