Question

5. The force F is given by Stoke's equation: F = 6nry Then the dimension of viscosity coefficient n are
(a) (ML-1T-1)
(b) (MLT-1)
(c) [M-1 L-1 T-1 ]
(d) [ ML2T-1]​

Answer 1

Given:

Stroke's Force :

$\rm F = 6\pi \eta rv$

To find:

Dimensions of $\eta$?

Calculation:

$\rm F = 6\pi \eta rv$

$\rm \implies \bigg[ F \bigg] = \bigg[\eta rv \bigg]$

$\rm \implies \bigg[ ML{T}^{ - 2} \bigg] = \bigg[\eta \times L \times L{T }^{ - 1} \bigg]$

$\rm \implies \bigg[ ML{T}^{ - 2} \bigg] = \bigg[\eta \times {L }^{2} {T }^{ - 1} \bigg]$

$\rm \implies \bigg[\eta\bigg] = \bigg[M{L}^{ - 1} {T}^{ - 1}\bigg]$

So, option a) is correct .