Question

A small metal ball of mass ‘m’ is dropped in a liquid contained in a vessel, attains a terminal velocity ‘v’. If a metal ball of same material but of mass ‘8m’ is dropped in same liquid then the terminal velocity will be ______.

Options

• v

• 2v

• 4v

• 8v

Answer 1

A small metal ball of mass ‘m’ is dropped in a liquid contained in a vessel, attains a terminal velocity ‘v’. If a metal ball of same material but of mass ‘8m’ is dropped in same liquid then the terminal velocity will be 4v.

Explanation:

For a small sphere falling in a liquid (Stokes’ law):

`v_t = (2r^2 (rho_s - rho_l)g)/(9eta)`

So, terminal velocity v_t​ ∝ r².

Now, mass of a sphere:

m ∝ r³

If mass becomes 8m, then:

r³ ∝ 8 ⇒ r = 2r

Since v_t ​∝ r²,

v_t ​∝ (2r)² = 4r²

So terminal velocity becomes 4 times.