Q 11-01-047JEE MainMedium
The viscous force on a small sphere moving slowly through a liquid depends on the coefficient of viscosity $\eta$, the radius $r$ of the sphere and its speed $v$ as $F = k\,\eta^a r^b v^c$, where $k$ is a dimensionless constant. Find the value of $a + b + c$.
Numerical value type. Enter your answer.
Answer: 3
$[\eta] = [ML^{-1}T^{-1}]$
$$[MLT^{-2}] = [ML^{-1}T^{-1}]^a\,[L]^b\,[LT^{-1}]^c$$
M: $a = 1$
T: $-a - c = -2 \Rightarrow c = 1$
L: $-a + b + c = 1 \Rightarrow b = 1$
So $F = k\eta r v$ (Stokes' law, with $k = 6\pi$), and $a + b + c = 3$.
Solution by Sreeraj P, M.Sc Physics