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Two solid spheres of same metal but of mass $\mathrm{M}$ and $8 \mathrm{M}$ fall simultaneously on a viscous liquid and their terminal velocities are $v$ and $n v$ then value of $n$ is
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The correct answer is:
4
$$
\begin{aligned}
& \text { Hints: } m=\frac{4}{3} \pi r^3 \times \rho \\
& m \propto r^3 \\
& \left(\frac{r_1}{r_2}\right)^3=\frac{1}{8} \\
& \frac{r_1}{r_2}=\frac{1}{2} \\
& 6 \pi n r \mathrm{~V}=\frac{4}{3} \pi r^3(d=\rho) \\
& \mathrm{V} \propto r^2, \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\frac{1}{4} \\
& n=4
\end{aligned}
$$
\begin{aligned}
& \text { Hints: } m=\frac{4}{3} \pi r^3 \times \rho \\
& m \propto r^3 \\
& \left(\frac{r_1}{r_2}\right)^3=\frac{1}{8} \\
& \frac{r_1}{r_2}=\frac{1}{2} \\
& 6 \pi n r \mathrm{~V}=\frac{4}{3} \pi r^3(d=\rho) \\
& \mathrm{V} \propto r^2, \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\frac{1}{4} \\
& n=4
\end{aligned}
$$
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