Suppose the dimensional formula for acceleration, velocity length are `alpha beta^(-2), alphabeta^(-1) and alpha gamma`. Then the dimensional formula for the coefficient of friction is

Options

A. `alpha beta gamma`
B. `alpha^(-1)beta^(@)gamma^(@)`
C. `alpha^(@)beta^(-1)gamma^(@)`
D. `alpha^(@)beta^(@)gamma^(@)`

Answer

D

Explanation

Here `[a]=LT^(-2)=alpha beta^(-2),[v]=LT^(-1)=alpha beta^(-1)impliesalpha=L,beta=T,L=alpha gamma," "gamma=L/(alpha)=L/L=1`
Coefficient of friction `mu=F/R=M^(@)L^(@)T^(@)`
Check all the four given expressions and find which one is dimensionless.