Question

A sphere of certain diameter, when towed submerged under water, experiences a drag force of 4 N at a velocity of 1.5 m/s. If another sphere of twice the diameter of the sphere referred to above, is towed with the same velocity in water, the drag force experienced by this sphere will be

• A. 8N
• B. 16N
• C. 24N
• D. 32N

Answer 1

The correct option is B 16N

$FD=C_D\times A\times \frac{1}{2}\times \rho \times V^2$

(Since sufficient data is not given, Assume $C_D=Constant.)$

$Then{F}_D\propto A$

$F_D\propto D^2$

$\frac{F_{D_1}}{F_{D_2}}={\left(\frac{D_1}{D_2}\right)}^2$

$\frac{F_{D_1}}{F_{D_2}}={\left(\frac{D}{2D}\right)}^2$

$F_{D_2}=4F_{D_1}$

$F_{D_2}=4\times 4N=16N$