A raindrop reaching the ground with terminal velocity has momentum p . Another drop of twice the radius, also reaching the ground with terminal velocity, will have momentum

Question

A raindrop reaching the ground with terminal velocity has momentum p . Another drop of twice the radius, also reaching the ground with terminal velocity, will have momentum (A) 4p (B) 8p (C) 16p (D) 32p

Tardigrade Admin · Accepted Answer

As v propto r2 and the mass of the drop m propto r3 , its momentum p=mv propto r5 . Here, 25=32 .

Q. A raindrop reaching the ground with terminal velocity has momentum $p$ . Another drop of twice the radius, also reaching the ground with terminal velocity, will have momentum

$4 p$

$8 p$

$16 p$

$32 p$

As $v \propto r^{2}$ and the mass of the drop $m \propto r^{3}$ , its momentum $p = m v \propto r^{5}$ . Here, $2^{5} = 32$ .

Q. A raindrop reaching the ground with terminal velocity has momentum p . Another drop of twice the radius, also reaching the ground with terminal velocity, will have momentum

4p

8p

16p

32p