In the figure shown a uniform ringh of mass `m` placed on arough horizontal fixed surface. The coefficient of friction between left half of ring and table is `mu_(1)` whereas between right half and table is `mu_(2)` at the moment shown. The ring has angular velocity in clockwise sence in the figure shown. at this moment find the magnitude of acceleration ( in `m//s^(2)`) of centre `C` of ringe. [Given `g=10 m//s^(2)`]

Answer

`(mu_(2) - mu_(1))g/pi`

Explanation

Net force,
`F=2int_(0)^(2pi//2)(mu_(1)Rd theta)g cos theta`
`-2int_(0)^(pi//2)(mu_(1)R d thetalambda) g cos theta`
`=2(mu_(1)-mu_(2)).Rlambdag uarr`
`:. A=F/m=((2mu_(1)-mu_(2))R lambdag)/(2piR lambda)`
`=((mu_(1)-mu_(2))g)/(pi)=4`