Question

A sphere of radius $10$ cm and density $500kg/m^3$ is under water of density $1000kg/m^3$. The acceleration of the sphere is $9.80m/s^2$ upward. Viscosity of water is $1.0$ centipoises. If $g=9.81m/s^2$, the velocity of sphere is:

• A. $9$ m/s
• B. $10$ m/s
• C. $11$ m/s
• D. $12$ m/s

Answer 1

The correct option is C $11$ m/s

$\text{Weknow that}$

$f_{net}=Boyuncy-mg-dragforce$

$\frac{4}{3}\pi (0.1{)}^3\times 500\times 9.8=1000\times \frac{4}{3}\pi (0.1{)}^3\times 9.81-500\times \frac{4}{3}\pi (0.1{)}^3\times 9.81-6\pi \times {10}^{-3}\times V\times 0.1$

$6\pi \times {10}^{-3}v=500\times \frac{4}{3}\pi \left(0.1{)}^2\right(0.01)$

$V=\frac{\mathrm{100}}{9}=11m/sec$

Ans $:\left(c\right)$