A tiny ball of mass 100 g and density 2 g / cm 3 is dropped in a tall jar of oil of density 0.8 g / cm 3. When the ball acquires terminal velocity, the magnitude of the viscous force acting on it in dyne is.

Question

A tiny ball of mass 100 g and density 2 g / cm 3 is dropped in a tall jar of oil of density 0.8 g / cm 3. When the ball acquires terminal velocity, the magnitude of the viscous force acting on it in dyne is. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

When the ball falls with constant velocity, then viscous force is equal to effective weight of the ball.
Volume of the ball

= V = \frac{m}{ρ _{ball}} = \frac{100}{2} = 50 c m^{3}

Mass of the liquid displaced by the ball

= m^{'} = V ρ_{L i q} = 50 \times 0.8 = 40 g

∴

Viscous force

F = m g - m^{'} g

= (50 - 40) 980

= 9800 d y n e

Q. A tiny ball of mass 100g and density 2g/cm3 is dropped in a tall jar of oil of density 0.8g/cm3. When the ball acquires terminal velocity, the magnitude of the viscous force acting on it in dyne is________.

When the ball falls with constant velocity, then viscous force is equal to effective weight of the ball. Volume of the ball =V=ρball ​m​=2100​=50cm3 Mass of the liquid displaced by the ball =m′=VρLiq​=50×0.8=40g ∴ Viscous force F=mg−m′g =(50−40)980 =9800dyne

Q. A tiny ball of mass $100 g$ and density $2 g / c m^{3}$ is dropped in a tall jar of oil of density $0.8 g / c m^{3}$ . When the ball acquires terminal velocity, the magnitude of the viscous force acting on it in dyne is________.