Question

A spherical body of mass $m$ and radius $r$ is allowed to fall in. a medium of viscosity $\eta$. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called time constant $\tau$. Dimensionally, $\tau$ can be represented by (Given $[\eta] =$ $[ML^{-1}T^{-1}]$)

• A. $\frac{mr^{2}}{6\pi\eta}$
• B. $\sqrt{\left(\frac{6\pi mr\eta}{g^{2}}\right)}$
• C. $\frac{m}{6\pi\eta rv}$
• D. none of these

Answer 1

Answer: (D)

none of these

Answer 2

None of the expressions has the dimensions of time.