A sphere of radius R is gently dropped into liquid of viscosity η 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

Question

A sphere of radius R is gently dropped into liquid of viscosity η 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) 2 v (C) 4 v (D) 9 v

Tardigrade Admin · Accepted Answer

Terminal velocity v propto r2 ∴ (v'/v)=((2 R)2/(R)2) or v' = 4 v

Q. A sphere of radius $R$ is gently dropped into liquid of viscosity $η$ 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

v

2 v

4 v

9 v

Terminal velocity $v \propto r^{2}$
$∴ \frac{v ^{'}}{v} = \frac{( 2 R ) ^{2}}{( R ) ^{2}}$
or $v^{'} = 4 v$

Q. A sphere of radius R is gently dropped into liquid of viscosity η in a vertical uniform tube. It attains a terminal velocity v. Another sphere of radius 2R when dropped into the same liquid, will attain its terminal velocity

v

2 v

4 v

9 v

Terminal velocity v∝r2 ∴vv′​=(R)2(2R)2​ or v′=4v

Q. A sphere of radius $R$ is gently dropped into liquid of viscosity $η$ 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

Terminal velocity $v \propto r^{2}$
$∴ \frac{v ^{'}}{v} = \frac{( 2 R ) ^{2}}{( R ) ^{2}}$
or $v^{'} = 4 v$