Question

Q. 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

Solution:
$$
\begin{aligned}
&\text { Here, }[a]=L T^{-2}=\left(a \beta^{-2}\right) \\
&{[v]=L T^{-1}=a \beta^{-1}} \\
&\therefore \quad a=L, \beta=T \\
&{[L]=a \gamma} \\
&\therefore \quad \gamma=\frac{[L]}{\alpha}=\frac{L}{L}=1
\end{aligned}
$$
Coefficient of friction,
\(\mu=\frac{F}{R}=M^{0} L^{0} T^{0}\) i.e. dimensionless
Now, \(\alpha^{0} \beta^{0} \gamma^{-1}=L^{0} T^{0}(1)^{-1}=1\),
which is dimensionless.

Answer 2

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Answer 3

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