Question

A copper ball of radius $r$ is moving with a uniform velocity $v$ in the mustard oil and the dragging force acting on the ball is $F$. The dragging force on the copper ball of radius $2r$ with uniform velocity $2v$ in the mustard oil is

• A. $F$
• B. $2F$
• C. $4F$
• D. $8F$

Answer 1

The correct option is C $4F$

From Stoke's law, dragging force $F=6\pi \eta rv$
Where, $\eta$ is coefficient of viscosity.
Drag force on second copper ball $F^{\prime }=6\pi \eta \left(2r\right)\left(2v\right)=6\pi \eta rv\times 4$
Thus we get $\frac{F^{\prime }}{F}=4$
$⟹F^{\prime }=4F$.