Question

solve the question plz fast

Answer 1

you didn't mention about what is coefficient of ?

But according to symbol , I think
you said coefficient of viscosity .

we know,
F = 6πnrv
so, dimension of n = [ MLT-²]/[L²T-¹]
= [ML-¹T-¹ ]

now,
A/C to question
n depends upon
(1) Force/Area
(2) velocity gradient

so,

dimesion of n = K×[ dimension of {F/A} ]^a×[ dimension of velocity gradient ]^b

[ML-¹T-¹] = K [ML-¹T-²]^a × [T-¹]^b

[ML-¹T-¹] = K [M^a L^-a T^(-2a -b)]

compare both sides ,

a = 1 and -(2a + b) = -1
b = -1

hence,
coefficient of viscosity =K× {Force/A}/{velocity gradient }
e.g
n = K.F/A.velocity gradient