A uniform disc of mass m and radius R is projected horizontally with velocity v0 on a rough horizontal floor so that it starts off with a purely translatory motion at t = 0. After t0=v0nμg second it acquires a purely rolling motion as shown in figure. Find the value of n. [μ : coefficient of friction between disc and floor]

v = v0−μgt0 ω=αt0 α=2μgR v0−μgt0=2μgt0

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A uniform disc of mass m and radius R is projected horizontally with velocity $v_{0}$ on a rough horizontal floor so that it starts off with a purely translatory motion at t = 0. After $t_{0} = \frac{v_{0}}{n μ g}$ second it acquires a purely rolling motion as shown in figure. Find the value of n. [ $μ$ : coefficient of friction between disc and floor]

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Detailed Solution

${v = v}_{0} - μ g t_{0} {ω=αt}_{0} α= \frac{2μg}{R} v_{0} - μ g t_{0} = 2 μ g t_{0}$

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