Question

The dimensional formula for acceleration, velocity and length are $a{\beta }^{-2},a{\beta }^{-1}$ 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, $\left[a\right]=L{T}^{-2}=\left(a{\beta }^{-2}\right)$
$\left[\upsilon \right]=L{T}^{-1}=a{\beta }^{-1}$
$\therefore a=L,\beta =T$
$\left[L\right]=a\gamma$
$\therefore \gamma =\frac{\left[L\right]}{\alpha }=\frac{L}{L}=1$
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.