Question

a sphere of radius 'a' moves with a velocity v in the medium amd the force F acting on it is given by F = 6phav. The dimensions of h is ?​

Answer 1

Given:

A sphere of radius 'a' moves with a velocity v in the medium amd the force F acting on it is given by F = 6phav.

To find:

Dimensions of h

Calculation:

Dimension of any equation will be same on LHS and RHS:

LHS:

$\bigg\{F\bigg\} = \bigg\{ML{T}^{-2}\bigg\}$

RHS:

$\bigg \{6 \rho hav \bigg \}$

$= \bigg \{ \rho \times h \times a \times v \bigg \}$

$= \bigg \{M{L}^{ - 3} \times (h) \times L \times L{T}^{ - 1} \bigg \}$

$= \bigg \{M{L}^{ - 3} \times (h) \times {L}^{2} {T}^{ - 1} \bigg \}$

$= \bigg \{M{L}^{ - 1} {T}^{ - 1} \times (h) \bigg \}$

Equating LHS and RHS:

$\bigg\{ML{T}^{-2} \bigg \}= \bigg \{M{L}^{ - 1} {T}^{ - 1} \times (h) \bigg \}$

$= > \bigg \{h \bigg \} = \bigg \{{L }^{2} {T}^{ - 1} \bigg \}$

So, final answer is:

$\boxed{ \sf{ \red{\bigg \{h \bigg \} = \bigg \{{L }^{2} {T}^{ - 1} \bigg \}}}}$