Question 27

A small metallic sphere of diameter 2 mm and density $$10.5 g/cm ^{3}$$ is dropped in glycerine having viscosity 10 Poise and density $$1.5 g/cm^{3}$$ respectively. The terminal velocity attained by the sphere is __ $$cm/s$$.
$$(\pi=\frac{22}{7} \text { and } g=m/s^{2})$$

Using Stokes' law: $$v_t = \frac{2r^2(\rho_s - \rho_l)g}{9\eta}$$

r = 1 mm = 0.1 cm, ρ_s = 10.5 g/cm³, ρ_l = 1.5 g/cm³, η = 10 P = 10 g/(cm·s), g = 980 cm/s².

$$v_t = \frac{2 \times 0.01 \times 9 \times 980}{9 \times 10} = \frac{176.4}{90} = 1.96 \approx 2.0$$ cm/s

The answer is Option 2: 2.0 cm/s.

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A small metallic sphere of diameter 2 mm and density $$10.5 g/cm ^{3}$$ is dropped in glycerine having viscosity 10 Poise and density $$1.5 g/cm^{3}$$ respectively. The terminal velocity attained by the sphere is __ $$cm/s$$.$$(\pi=\frac{22}{7} \text { and } g=m/s^{2})$$