Two wheels A and B of same radii starts rolling with same angular velocity up a rough inclined and smooth inclined plane respectively. The angle of inclination of both the planes is same.
Column-I Column-II
i. the maximum height gained depends upon p. angular velocity
ii. The retarding force for translational velocity is more for q. translational velocity
iii. The wheel which will go upto to a greater height rolls up on a r. rough inclined plane
iv. The maximum height gained does not depend s. smooth inclined plane
Now match the given columns and select the correct option from the codes given below.

Moderate

Solution

The maximum height gained depends upon translational velocity. The retarding force for translational velocity is more for smooth inclined plane.
Retarding force for translational velocity for wheel A ,is lesser than B as the friction support rolling
Retarding force for translational velocity for wheel B = mg sin $θ$
If s be the maximum length of path traversed by the wheel , a be the deceleration then 0= $0 = v^{2} - 2 a s w h e r e s = h / S i n θ .$ So maximum height h is independent of angular velocity.

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	Column-I		Column-II
i.	the maximum height gained depends upon	p.	angular velocity
ii.	The retarding force for translational velocity is more for	q.	translational velocity
iii.	The wheel which will go upto to a greater height rolls up on a	r.	rough inclined plane
iv.	The maximum height gained does not depend	s.	smooth inclined plane