Question

The dimensional formula for acceleration, velocity and length are $aβ^{-2}, \,aβ^{-1}$ 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, $\left[a\right] = LT^{-2 }=\left(aβ^{-2}\right)$
$\left[\upsilon\right] = LT^{-1} = aβ^{-1}$
$\therefore \quad a = L, β = T$
$\left[L\right] = a\gamma$
$\therefore \quad\gamma = \frac{\left[L\right]}{\alpha} = \frac{L}{L} = 1$
Coefficient of friction,
$\mu = \frac{F}{R} =M^{0}L^{0}T^{0}$ i.e. dimensionless
Now, $\alpha^{0}\beta^{0}\gamma^{-1} = L^{0}T^{0}\left(1\right)^{-1} = 1$,
which is dimensionless.