Question

A sphere of radius R is gently dropped into liquid of viscosity(n) 'ita' in a vertical uniform tube. It attains a terminal velocity v. Another sphere of radius 2 R when dropped into the same liquid, will attain its terminal velocity
(a) v
(b) 2v
(c) 4V
(d) 9v​

Answer 1

Given:

A sphere of radius R is gently dropped into liquid of viscosity(n) 'ita' in a vertical uniform tube.

It attains a terminal velocity v.

To find:

Another sphere of radius 2 R when dropped into the same liquid, will attain its terminal velocity

Solution:

From given, we have,

A sphere of radius R is gently dropped into liquid of viscosity(n)

Another sphere of radius 2 R dropped into the same liquid,

The terminal velocity is directly proportional to the radius of the sphere.

So, we have,

terminal velocity v ∝ r²

⇒ For the sphere of radius R, we have,

v ∝ R²

⇒ For the sphere of radius 2R, we have,

v ∝ (2R)²

= v ∝ 4R²

∴ v = 4v

Option (c) 4V is correct option.