Question

The dimensional formula for acceleration, velocity and length are $\alpha {\beta }^{-2},\alpha {\beta }^{-1}$ and $\alpha \gamma .$ What is the dimensional formula for the coefficient of friction?

• A. $\alpha \beta \gamma$
• B. ${\alpha }^{-1}{\beta }^0{\gamma }^0$
• C. ${\alpha }^0{\beta }^{-1}{\gamma }^0$
• D. ${\alpha }^0{\beta }^0{\gamma }^{-1}$

Answer 1

Answer: (D)

Here $,a=L{T}^{-2}=\alpha {\beta }^{-2};v=L{T}^{-1}=\alpha {\beta }^{-1}$
$\therefore \alpha =L,\beta =T,L=\alpha \gamma$
$\therefore \gamma =\frac{L}{\alpha }=\frac{L}{L}=1$
Coefficient of friction, $\mu =\frac{F}{R}=\left[M^0{L}^0{T}^0\right]$
Check all the four given expressions and find which one is dimensionless.
${\alpha }^0{\beta }^0{\gamma }^{-1}=\left[L^0{T}^0(1{)}^{-1}\right]=1,$ which is dimensionless.