A unifromsphereof massm andradiusR is placed ona rough horizontalsurface(figure).thesphere isstuuck horizontally at a heighth fromthefloor . Match the following

A unifromsphereof massm andradiusR is placed ona rough horizontalsurfa

1.	A unifromsphereof massm andradiusR is placed ona rough horizontalsurface(figure).thesphere isstuuck horizontally at a heighth fromthefloor . Match the following
Answer» Solution :Considerthe diagramwherea sphere ofm andradius ,R, struckhorizontally atheighthabove thefloor the spherewillrollwithoutsippingwhen `omega=(v)/( R)` , WHEREV islinear velocityand `omega` is angular velocity of thesphere Now , angular momentumof sphere, aboutcentreof mass ( [We areapplyingconservationof angular momentumjustmomentumjustbeforeandafter struck ] `mv(h-R)=Iomega=((2)/(5)mR^(2))((v)/(R))` ` impliesmv(h-R)=(2)/(5)MVR` `h-R=(2)/(5)Rimplies h=(7)/(5) R` Thereforethesphereeill rollwithout sippingwitha constantvelocityandhence, noloss ofenergy,so`(D) to (i)` Torquedueto appliedforce,F aboutcentre ofmass For `tau=0,h=R` ,spherewillhaveonlytranslational motion. itwould loseenergy byfriction hence, `(B ) to (iv)` thesphere willspinclokwisewhen`taugt 0implies hgt R` therefore , ` (C ) to (II)` the spherewill spinanti- clockwisewhen`tault 0implies hltR,(a) to (iii)`