Correct Answer - Option 1 : 1 : 4
CONCEPT:
-
Terminal velocity: It is the maximum velocity that an object attained when it falls through a fluid.
- It occurs when the sum of the viscous force (Fv) and the buoyancy (FB) is equal to the downward force of gravity (Fg) acting on the object.
Fg = FB + Fv
mg = FB + Fv
\(\frac{4}{3}\pi r^3 ρ g = \frac{4}{3}\pi r^3 σ g - 6 \pi η rv\)
\(v=\frac{2}{9} r^2g \left ( \frac{σ - ρ}{η} \right )\)
where v is the terminal velocity, r is the radius of the object, g is the gravitational acceleration, ρ and σ are the density of the medium and object, and η is the viscosity of the medium.
CALCULATION:
Given that radius are r and 2r. So \( {r_1 \over r_2}= {1 \over 2}\)
Terminal velocity v is given by:
\(v=\frac{2}{9} r^2g \left ( \frac{σ - ρ}{η} \right )\)
v α r2 (since all other parameters are the same for both the drops)
\({v_1 \over v_2} = \frac{r_1^2}{r_2^2}= \frac{1^2}{2^2}= \frac{1}{4}\)
So the correct answer is option 1.