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good morning sir please explain this problem problem is given in image please explain it fast

good morning sir please explain this problem problem is given in image please explain it fast

Question Image
Grade:12

1 Answers

Ravneet
104 Points
3 years ago
Answer 15. 
WHEN THE ELECTRIC FIELD IS APPLIED,  
  • IT WILL PRODUCE TORQUE (there will be friction also due to rough horizontal surface )
  • THE NET ELECTRIC FORCE WILL BE ZERO.   
torque = R . F. sinx                                              where F is qE but q is not given 
so q = (lambda)(R.dx)        where x is the angle where the charge is distributed 
TARGET: TO find TORQUE independent of x (angle)
torque = ∫ (lambda . R .dx ) E sinx 
limit of integration will be 0 to pi/ 2 and this torque will be multiply by 2 becouse the torque is produced by both + and – charge 
torque = 2 X ∫ (lambda . R .dx ) E sinx             limit of integration will be 0 to pi/ 2 
ON SOLVING, WE GET 
torque = (2)( lambda)(  E )( R2)
AS THE MOTION IS PURE ROLLING,
torque – (torque produced by frictional force ) = (moment of inertia ) (alpha ) 
                                                     where alpha = angular acceleration = f/(mR)
 
 (2)( lambda)(  E )( R2)    –  f(R)    =   I (ALPHA )
  (2)( lambda)(  E )( R2)    –  f(R)    =    I X f/(mR)
PUT I = mR2
and sove for f (frictional force)
f = (lambda )(E)(R)__________________________ANSWER 

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