Fluids - 12. Problems Based on Terminal Velocity

This video explains the following :
1) Problems Based on Terminal Velocity
Que: If the terminal speed of a sphere of gold (density = 19.5 kgm−3) is 0.2 ms−1 in a viscous liquid (density = 1.5 kgm−3), find the terminal speed of a sphere of silver (density = 10.5 kg/m3) of the same size in the same liquid.
(a) 0.4 ms−1
(b) 0.133 ms−1
(c) 0.1 ms−1
(d) 0.2 ms−1
Que: If a ball of steel (density, ρ= 7.8g cm−3) attains a terminal velocity of 10 cms −1 when falling in a tank of water (coefficient of viscosity ηwater = 8.5 × 10−4 Pa-s), then its terminal velocity in glycerine (ρ= 1.2 g cm-3, η= 13.2 Pa-s) would be nearly
(a)1.6 x 10-5 cm s −1
(b) 6.25 x 10-5 cm s −1
(c) 6.45 x 10-5 cm s −1
(d)1.5 x 10-5 cm s −1
Que: A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to
a) r3
b) r2
c) r5
d) r4
Que: A solid sphere of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2 when falling through the same fluid, the ratio (v1 /v2) equals
(a) 9
(b) 1/27
(c) 1/9
(d) 27
Que: A spherical ball is dropped in a long column of a viscous liquid. The speed (v) of the ball as a function of time (t) may be best represented by