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)
• B. (p-w) (q-x,y) (r-w,y) (s-w,z)
• C. (p-y,z) (q-y,z) (r-w,x) (s-y)
• D. (p(w,x) (q-w,x) (r-w,x) (s-w,x)

Answer 1

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:

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

(q) L = MvR - $I\omega =MvR-I\left(\frac{2v}{R}\right)$

= MvR - 2MvR $<$ 0 for ring

$\Rightarrow v_{cm}$ right

=MvR - $\left(\frac{4}{5}\right)MvR>0$ for solid sphere

$\Rightarrow v_{cm}$ left

(r) Angular momentum about lowest point:

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

(s) L=MvR - $I\omega =MvR-I\left(\frac{v}{2R}\right)>0$

For both ring and sphere.