Question

Two spherical rain drops of radii in the ratio 4:5 are falling vertically through air. The ratio of the terminal velocities of the rain drops is:

• A. \( 64:125 \)
• B. \( 16:25 \)
• C. \( 4:5 \)
• D. \( 1:1 \)

Hint:

For spherical objects falling through a fluid, the terminal velocity is proportional to the square of the radius.

Answer 1

The Correct Option is B

Step 1:
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 sphere.
Step 2:
Given the ratio of the radii \( r_1/r_2 = 4/5 \), the ratio of the terminal velocities is: \[ \frac{v_{t1}}{v_{t2}} = \left( \frac{r_1}{r_2} \right)^2 = \left( \frac{4}{5} \right)^2 = \frac{16}{25} \]
Step 3:
Thus, the ratio of the terminal velocities is \( 16:25 \).