JEE Advance - Physics (2016 - Paper 1 Offline - No. 3)
Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm–3 and viscosity $$\eta $$ = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm–3 and viscosity $$\eta $$ = 2 poiseulles. The ratio of the terminal velocities of P and Q is
Answer
3
Explanation
Terminal velocity is given by
$${v_T} = {2 \over 9}{{{r^2}} \over \eta }(d - \rho )g$$
$${{{v_P}} \over {{v_Q}}} = {{r_P^2} \over {r_Q^2}} \times {{{\eta _Q}} \over {{\eta _P}}} \times {{(d - {\rho _P})} \over {(d - {\rho _Q})}}$$
$$ = {\left( {{1 \over {0.5}}} \right)^2} \times \left( {{2 \over 3}} \right) \times {{(8 - 08)} \over {(8 - 1.6)}} = 4 \times {2 \over 3} \times {{7.2} \over {6.4}} = 3$$
$${v_T} = {2 \over 9}{{{r^2}} \over \eta }(d - \rho )g$$
$${{{v_P}} \over {{v_Q}}} = {{r_P^2} \over {r_Q^2}} \times {{{\eta _Q}} \over {{\eta _P}}} \times {{(d - {\rho _P})} \over {(d - {\rho _Q})}}$$
$$ = {\left( {{1 \over {0.5}}} \right)^2} \times \left( {{2 \over 3}} \right) \times {{(8 - 08)} \over {(8 - 1.6)}} = 4 \times {2 \over 3} \times {{7.2} \over {6.4}} = 3$$
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