Eight equal drops of water are falling through air with a steady velocity of 10 cm s-1. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is

Question

Eight equal drops of water are falling through air with a steady velocity of 10 cm s-1. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is (A) 40 cm s-1 (B) 10 cm s-1 (C) 30 cm s-1 (D) 80 cm s-1

Tardigrade Admin · Accepted Answer

Here, v propto r2 ∴ (v1/v2) =(r12/82 / 3 ⋅ r2) (10/v2) =(1/4) v2 =40 cm / s

Q. Eight equal drops of water are falling through air with a steady velocity of $10 c m s^{- 1}$ . If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is

$40 c m s^{- 1}$

$10 c m s^{- 1}$

$30 c m s^{- 1}$

$80 c m s^{- 1}$

Here,
$v \propto r^{2}$
$∴ \frac{v _{1}}{v _{2}} = \frac{r _{1}^{2}}{8 ^{2/3} \cdot r ^{2}}$
$\frac{10}{v _{2}} = \frac{1}{4}$
$v_{2} = 40 c m / s$

Q. Eight equal drops of water are falling through air with a steady velocity of 10cms−1. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is

40cms−1

10cms−1

30cms−1

80cms−1