Question

2.1

Given that the speed of light, v, in a fluid depends on an elastic modulus, T. with

dimensions ML-'T-2 and the fluid density, p, in the form v = (T)°(p). If this is to be a

dimensionally homogeneous equation, determine the values of a and b and write the

simplest form of an equation for the speed of light, W.

(4)

Answer 1

Step-by-step explanation:

`v = T^a* \rho^b`

Using dimensional formula on both sides ,

LT⁻¹ =
`(ML^(-1)T^(-2))^a(ML^(-3))^b`

=
`M^(a+b)L^(-a-3b)T^(-2a)`

equating the power of equal terms

- 2 a = -1

a = 0.5

-0.5 -3b = 1

3b = -1.5

b = -0.5

a + b = 0

Hence

a = 0.5

b = -0.5

`v=\sqrt{(T)/(\rho) }`