Question

A small metallic sphere of diameter 2 mm and density 10.5 g/cm$^3$ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm$^3$ respectively. The terminal velocity attained by the sphere is ___ cm/s. ($\pi = \frac{22}{7}$ and $g = 10$ m/s$^2$)

• A. 1.5
• B. 2.0
• C. 3.0
• D. 1.0

Hint:

Ensure all units are consistent (CGS). 1 Poise = 1 dyne$\cdot$s/cm$^2$. $g=1000$ cm/s$^2$.

Answer 1

The Correct Option is B

Radius $r = 1$ mm $= 0.1$ cm.
Formula: $v_t = \frac{2r^2 g (\rho - \sigma)}{9\eta}$.
Convert units to CGS: $\eta = 10$ Poise, $g = 1000$ cm/s$^2$.
$v_t = \frac{2 (0.1)^2 (1000) (10.5 - 1.5)}{9 (10)}$.
$v_t = \frac{2 (0.01) (1000) (9)}{90} = \frac{180}{90}$.
$v_t = 2$ cm/s.