Question

Dimensions $\left[ ML ^{-1} T ^{-1}\right]$ are related to

• A. torque
• B. work
• C. energy
• D. coefficient of viscosity

Answer 1

Answer: (D)

coefficient of viscosity

Answer 2

Torque is defined as $\vec{\tau}=\vec{r} \times \vec{F}$ $\therefore$ Dimensions of torque $[\tau]=[r] \times[F]$ $=[ L ] \times\left[ MLT ^{-2}\right]$ $=\left[ ML ^{2} T ^{-2}\right]$ Similarly for work and energy the dimensions are same as that of torque i.e. $\left[ ML ^{2} T ^{-2}\right]$ Now for viscosity, we know that $F =6 \pi \eta r$ $\Rightarrow \eta =\frac{F}{6 \pi r}$ $\therefore[\eta] =\frac{F}{[r][v]}=\frac{\left[M L T^{2}\right]}{[L]\left[L T^{-1}\right]}$ $=\left[M L^{-1 T-1}\right]$ $\therefore$ The given dimensions are related to the coefficient of viscosity.