Question

Two rain drops falling through air have radii in the ratio 1:2. They will have terminal velocity in the ratio

• A. 1:2
• B. 4:1
• C. 1:4
• D. 2:1

Hint:

The terminal velocity of a falling object is proportional to the square of its radius. This is important when comparing the velocities of different-sized objects.

Answer 1

The Correct Option is C

Step 1: Terminal velocity and radius.
The terminal velocity \( v_t \) of a spherical object falling through a fluid is given by: \[ v_t \propto r^2 \] where \( r \) is the radius of the object. This relation comes from the balance between the gravitational force and the drag force acting on the object.
Step 2: Using the given ratio of radii.
Let the radii of the two rain drops be \( r_1 \) and \( r_2 \), where \( r_2 = 2r_1 \). The ratio of their terminal velocities will be: \[ \frac{v_{t2}}{v_{t1}} = \left( \frac{r_2}{r_1} \right)^2 = \left( \frac{2r_1}{r_1} \right)^2 = 4 \]
Step 3: Conclusion.
Thus, the ratio of their terminal velocities is \( 1:4 \), which corresponds to option (C).