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Physics · PYQ NEET UG 2019(2)
हिन्दीTwo 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 \( 1 \text{ mm} \) and \( 2 \text{ mm} \), 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,
Correct answer · Option 2
\( \frac{79}{72} \)
Explanation
Terminal velocity \( v_t = \frac{2r^2(\rho - \sigma)g}{9\eta} \). Since mass \( m = \frac{4}{3}\pi r^3 \rho \) is equal, \( \rho \propto 1/r^3 \). Substituting \( r_1 = 1 \), \( r_2 = 2 \), \( \rho_1 = 8\rho_2 \), \( \sigma = 0.1\rho_2 \), ratio comes out to be \( 79/72 \).
