The dimensional formula for acceleration, velocity and length are `alphabeta^(-2)`, `(alphabeta)^(-1)` as and `alphagamma`. What is the dimensional formula for the coefficient of friction?

Options

A. `alphabetagamma`
B. `alpha^(-1)beta^(0)gamma^(0)`
C. `alpha^(0)beta^(-1)gamma^(0)`
D. `alpha^(0)beta^(0)gamma^(-1)`

Answer

D

Explanation

Here, `a= LT^(-2)= alphabeta^(-2), v= LT^(-1)= alphabeta^(-1)`
`:. alpha= L, beta= T, L= alphagamma :. Gamma =(L)/(alpha)= (L)/(L)= 1`
Coefficient of friction `mu= (F)/(R)= [M^(0)L^(0)T^(0)]`
Check all the four given expressions and find which one is dimensionless.
`alpha^(0)beta^(0)gamma^(-1)= [L^(0)T^(0)(1)^(-1)]=1` Which is dimensionless.