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Question

Consider a wheel purely rolling on a rough horizontal surface with constant velocity v. Radius of the wheel is R and C is the center of wheel. M is top-most point, P is bottom-most point and N is in level with C at any time. Match the columns for this instant of time.


A

(p-w,x); (q-x,y); (r-w,x); (s-w,x)

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B

(p-w) (q-x,y) (r-w,y) (s-w,z)

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C

(p-y,z) (q-y,z) (r-w,x) (s-y)

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D

(p(w,x) (q-w,x) (r-w,x) (s-w,x)

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Solution

The correct option is A

(p-w,x); (q-x,y); (r-w,x); (s-w,x)


(p-w,x); (q-x,y); (r-w,x); (s-w,x)

Take anticlockwise positive

(p) Angular momentum about lowest point:

L=mVr+Iω>0, so final velocity on pure rolling should be towards left for any body for L to be positive.

(q) L = MvR - Iω=MvRI(2vR)

= MvR - 2MvR < 0 for ring

vcm right

=MvR - (45)MvR>0 for solid sphere

vcm left

(r) Angular momentum about lowest point:

L = MvR + Iω>0, so final velocity on pure rolling should be towards left for any body for L to be positive.

(s) L=MvR - Iω=MvRI(v2R)>0

For both ring and sphere.


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