Mechanical Properties of Fluids - Result Question 11
11. Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_1$ and $\rho_2(\rho_1=8 \rho_2)$ and have radii of $1 mm$ and 2 $mm$, respectively, they are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \rho_2$. The ratio of their terminal velocities would be,
[NEET Odisha 2019]
(a) $\frac{79}{36}$
(b) $\frac{79}{72}$
(c) $\frac{19}{36}$
(d) $\frac{39}{72}$
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Answer:
Correct Answer: 11. (a)
Solution:
- (a) Terminal velocity $V_T=(\rho-\sigma) g$
$V _{T_1}=\frac{2 \times(1)^{2}}{9 \eta}(\rho_1-0.1 \rho_2) g$
$V _{T_1}=\frac{2 \times 1}{9 \eta}(8 \rho_2-0.1 \rho_2) g$
$V _{T_2}=\frac{2 \times(2)^{2}}{9 \eta}(\rho_2-0.1 \rho_2) g$
$\therefore \quad \frac{V _{T_1}}{V _{T_2}}=\frac{7.9}{4(0.9)}=\frac{79}{36}$
