CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A cotton reel placed on a rough surface has an inner radius r and outer radius R . Mass of the reel is M and moment of inertia about longitudinal rotational axis is I. A force F is applied at the free end of thread wrapped on the reel as shown in figure. If the reel moves without sliding, then


A
areel=FR(Rr)I+MR2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
areel=FR(R+r)I+MR2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
αreel=F(R+r)I+MR2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Ffriction=F(1+MRr)I+MR2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D Ffriction=F(1+MRr)I+MR2

As the body rolls, point P will be instantaneous center of rotation (ICR). There is clockwise torque about ICR. Hence, center of mass will have acceleration in right direction and the reel will rotate in clockwise direction.

The equations of motion are
Fx=Ff=Ma .....(i)
Fy=NMg=0 ........(ii)
τ=f×RF×r=Iα .....(iii)

As the reel rolls without slipping, a=Rα

From eqs. (i) and (iii),
FfM=R(f×RF×r)I
f=F(1+MRr)I+MR2

Force of friction comes out to be positive, therefore our assumption about the direction of friction force was correct.

On substituting the expression for f in (i)
we obtain a=FM[1(1+MRr)I+MR2]

Also, α=aR=FMR[1(1+MRr)I+MR2]

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon