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.