GATE 2022 CE (CE2) – Question 58
Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. Assume Stokes’ law is valid. The drag force on particle Q will be________ times the drag force on particle P. (round off to the nearest integer)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 8
Explanation
For a settling sphere under Stokes’ law, terminal velocity is proportional to d². Drag is $3\pi\mu d v$, hence proportional to d³ at terminal settling.
Therefore $F_Q/F_P=(1.0/0.5)^3=\mathbf8$. This also follows by equating terminal drag to submerged weight.