Question

The force depends on coefficiant of viscosity , radius and velocity . Derive dimensional formula for force

Answer 1

Hey Dear,

◆ Answer -

F = k.ηvr

● Explaination -

First we'll write down dimensions of all quantities.

[F] = [L1M1T−2]

[η] = [L-1M1T-1]

[v] = [L1T-1]

[r] = [L]

Let the dimensional formula of force be -

F = k.η^x.v^y.r^z

Putting dimensions,

[L1M1T−2] = [L-1M1T-1]^x × [L1T-1]^y × [L]^z

[L1M1T−2] = [L^(-x+y+z).M^(x).T^(-x-y)

Comparing indexes,

-x + y + z = 1

x = 1

-x - y = -2

Solving these 3 equations,

x = 1

y = 1

z = 1

Therefore,

F = k.η^1.v^1.r^1

F = k.ηvr

* Constant k can be experimentally determined.

Thanks for asking..