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← JEE Advanced 2016 · Paper 1
PhysicsInteger+3Question 17 of 54

JEE Advanced 2016 · Paper 1, Physics question 17

Consider two solid spheres P and Q each of density 8 gm cm−38\ \mathrm{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−30.8\ \mathrm{gm\,cm^{-3}} and viscosity η=3\eta=3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm−31.6\ \mathrm{gm\,cm^{-3}} and viscosity η=2\eta=2 poiseulles. The ratio of the terminal velocities of P and Q is

Answer and worked solution

Official answer: 3

Terminal velocity.
vt=2r2(ρ−σ)g9η∝r2(ρ−σ)η.v_t=\frac{2r^2(\rho-\sigma)g}{9\eta}\propto\frac{r^2(\rho-\sigma)}\eta.

Ratio.
vPvQ=(0.5)2×7.2/3(0.25)2×6.4/2=0.60.2=3.\frac{v_P}{v_Q}=\frac{(0.5)^2\times7.2/3}{(0.25)^2\times6.4/2}=\frac{0.6}{0.2}=3.

Answer: 3

Topics:Terminal velocityViscosity and Stokes' law
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