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  • A small copper ball of mass m falls in a viscous liquid with terminal velocity v. Another spherical copper ball of mass M falls in the same liquid with terminal velocity nv where nn

A small copper ball of mass m falls in a viscous liquid with terminal velocity v. Another spherical copper ball of mass M falls in the same liquid with terminal velocity nv where n is a number. The ratio \mathrm{\frac{M}{m}}  is 

Option: 1

\mathrm{\sqrt{n}}


Option: 2

\mathrm{n}


Option: 3

\mathrm{n^{3 / 2}}


Option: 4

\mathrm{n^2}


Answers (1)

best_answer

Let r be the radius of the ball of mass m and R be the radius of the ball with mass M. Terminal velocity \propto r^2. Therefore
\mathrm{ \begin{aligned} \frac{n v}{v} & =\frac{R^2}{r^2} \\ \Rightarrow \quad \frac{R}{r} & =n^{1 / 2} \\ \text { Now } \quad \frac{M}{m} & =\frac{\frac{4 \pi}{3} \rho R^3}{\frac{4 \pi}{3} \rho r^3}=\frac{R^3}{r^3}=\left(\frac{R}{r}\right)^3=n^{3 / 2} \end{aligned} }
So the correct choice is (c).

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