A uniform circular disc of radius R is placed on a frictionless horizontal plane. Another identical disc rotating with angular velocity $ω_{0}^{}$ is gently placed on top of the first disc. The coefficient of friction between the discs is $μ$ .The time in which both the discs acquire same angular velocity is $n R ω_{0}^{} / 8 μ g$ . Find the value of n.

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answer is 3.

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Detailed Solution

Final angular speed $\frac{w_{0}^{}}{2}$
$∴ \int_{0}^{t} τ_{f}^{} Δ t = I_{c m}^{} \frac{ω_{0}^{}}{2}, w h e r e τ_{f}^{} = \frac{2}{3} μ m g R$
$\begin{array}{l} \Rightarrow \frac{2}{3} (μ m g R) t = \frac{m R^{2}}{2} . \frac{ω_{0}^{}}{2} \\ \Rightarrow t = \frac{3 R ω_{0}^{}}{8 μ g} \end{array}$

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