Most Important Selected Qs for JEE AdvancedPhysicsRotational Motion
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( R) .
Options
- AAngular acceleration of the disc at any instant is proportional to 1 R^3 , where R is radius of the ribboned d
- BAngular acceleration of the disc at any instant is proportional to 1 R^2 , where R is the radius of the ribbon
- CForce required to pull the ribbon at constant speed u is F= I u^2 d 2 R^4 .
- DForce required to pull the ribbon at constant speed u is F = Iu^2 ~d R^4 .
Correct answer
C. Force required to pull the ribbon at constant speed u is F= I u^2 d 2 R^4 .
Step-by-step solution
aligned & R=u= constant & d R d t +R d d t =0 & d d t =- R d R d t aligned In time dt radius decreases by dR aligned & -2 R d R=u d d t & d R d t =- u d 2 R & d d t = = R u d 2 R & = u^2 d 2 R^3 & = I u^2 d 2 R^3 & F= I u^2 d 2 R^4 aligned