An iron sphere of mass $20 \times {10^{ - 3}}$kg falls through a viscous liquid with terminal velocity $0.5{\rm{m}}{{\rm{s}}^{ - 1}}$. The terminal velocity $\left( {{\rm{inm}}{{\rm{s}}^{ - 1}}} \right)$ of another iron sphere of mass $54 \times {10^{ - 2}}$ kg is

JEE PHYSICS MCQ: MECHANICAL PROPERTIES OF FLUIDS

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Application +4 | -1

An iron sphere of mass

20 \times {10^{ - 3}}

kg falls through a viscous liquid with terminal velocity

0.5\mathrm{m}{\mathrm{s}^{ - 1}}

. The terminal velocity

\left( {\mathrm{inm}{\mathrm{s}^{ - 1}}} \right)

of another iron sphere of mass

54 \times {10^{ - 2}}

kg is

View answer and explanation

Correct option: A

4.5

Option A (4.5) is correct because terminal velocity is proportional to the square of the radius, and thus related to mass by

v \propto M^{2/3}

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80 \mathrm{~kg}

20 \mathrm{~cm}

0.5 \mathrm{~cm}

0.1 \mathrm{~cm}

15 \mathrm{~m} / \mathrm{s}

5 \mathrm{~m}

=10^{-2}

m_1

d_1

d_2

m_2