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Question

A solid sphere of mass ‘m’ and radius ‘R’ is kept on a rough surface. The velocities of air (density) around the sphere area as shown in the figure. Assuming ‘R’ to be small and m=4πρR2g kg, the minimum value of coefficient of friction so that the sphere starts pure rolling is 1β. (Assuming force due to pressure difference is acting on the centre of mass of the sphere), determine the value of β.___

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Solution

Force due to pressure difference is F=P×A
=12ρ(V22V21)×πR2,F=12ρ(147)×πR2=7πρR22
For translational motion F – f = ma . . . . .(1)
For rotational motion
f×R=Iα=IaR
f=IaR2=25mR2×aR2=25maF=ma+f=ma+25ma=75ma,ma=57Ff=25×57F=2F7=27×7πρR22f=πρR2μmg=πρR2μ=πρR2mg=14μ=14=1ββ=4

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