JEE Main202127 Jul 2021Evening ShiftPhysicsMechanical Properties of FluidsActual
A raindrop with radius R = 0 . 2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water f w = 1000 kg m - 3 and Density of air f a = 1 . 2 kg m - 3 , g = 10 m / s 2 Coefficient of viscosity of air = 1 . 8 × 10 - 5 N s m - 2
Options
- A250 . 6   m   s - 1
- B43 . 56   m   s - 1
- C4 . 94   m   s - 1
- D14 . 4   m   s - 1
Correct answer
C. 4 . 94   m   s - 1
Step-by-step solution
At terminal speed a = 0 F net = 0 mg = F v = 6 π η Rv V = mg 6 π η RV v = ρ w 4 π 3 R 3   g 6 π η R = 2 ρ w R 2   g 9 η = 400 81   m / s = 4 . 94   m / s