# A solid sphere, of radius R acquires a terminal velocity $\upsilon _{1}$ when falling (due to gravity ) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, $\upsilon _{2}$, when falling through the same fluid, the ratio $(\upsilon _{1}/\upsilon _{2})$ equals : Option 1) 9 Option 2) 1/27 Option 3) 1/9 Option 4) 27

$M=\rho \times \frac{4}{3}\pi R^{3}$

$\frac{M}{27}=\rho \times \frac{4}{3}\pi r^{3}$

$r\rightarrow \frac{R}{3}$

$V_{T}\alpha (Radius)^{2}$

$\frac{V_{T}}{V_{new}}=\frac{R^{2}}{(R/3)^{2}}=9$

Option 1)

9

Option 2)

1/27

Option 3)

1/9

Option 4)

27

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