A disc is free to rotate about an axis passing through its centre and perpendicular to its plane. The moment of inertia of the disc about its rotation axis is I. A light ribbon is tightly wrapped over it in multiple layers. The end of the ribbon is pulled out at a constant speed of u. Let the radius of the ribboned disc be R at any time and thickness of the ribbon be `d (lt lt R)`. Find the force (F) required to pull the ribbon as a function of radius R. A. Angular acceleration of the disc at any insant is proportional to `1/(R^(3))`, where `R` is radius of the ribboned discB. Angular acceleration o the disc at any instant is proportional to `1/(R^(2))` where `R` is the radius of the ribboned disc.C. Force required to pull the ribbon at constant speed `u` is `F=(Iu^(2)d)/(2piR^(4))`D. Force required to pull the ribbon at constant speed `u` is `F=(Iu^(2)d)/(piR^(4))`

A disc is free to rotate about an axis passing through its centre and

1.	A disc is free to rotate about an axis passing through its centre and perpendicular to its plane. The moment of inertia of the disc about its rotation axis is I. A light ribbon is tightly wrapped over it in multiple layers. The end of the ribbon is pulled out at a constant speed of u. Let the radius of the ribboned disc be R at any time and thickness of the ribbon be `d (lt lt R)`. Find the force (F) required to pull the ribbon as a function of radius R. A. Angular acceleration of the disc at any insant is proportional to `1/(R^(3))`, where `R` is radius of the ribboned discB. Angular acceleration o the disc at any instant is proportional to `1/(R^(2))` where `R` is the radius of the ribboned disc.C. Force required to pull the ribbon at constant speed `u` is `F=(Iu^(2)d)/(2piR^(4))`D. Force required to pull the ribbon at constant speed `u` is `F=(Iu^(2)d)/(piR^(4))`
Answer» Correct Answer - A::C `omegaR=u=`constant `omega(dR)/(dt)+R(domega)/(dt)=0` `:.(domega)/(dt)=-(omega)/R(dR)/(dt)` In time `dt` radius decreases by `dR` `-2pi RdR= uddt` `:.(dR)/(dt)=-(ud)/(2piR)` `(domega)/(dt)=alpha=(omega)/R (ud)/(2piR)` `alpha=(u^(2)d)/(2piR^(3))` `tau=(Iu^(2)d)/(2piR^(3))` `:.F=(Iu^(2)d)/(2piR^(4))`

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