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Question

# A wheel (to be considered as a ring) of mass m and radius R rolls without sliding on a horizontal surface R/2 at which it ascends without sliding.

A
the angular velocity of the ring just after it comes in contact with the step is 3 v/4 R
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B
the normal reaction due to the step on the wheel just after the impact is mg2+9mv216R
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C
the normal reaction due to the step on the wheel increases as the wheel ascends
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D
the friction will be absent during the ascent.
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Solution

## The correct options are A the angular velocity of the ring just after it comes in contact with the step is 3 v/4 R C the normal reaction due to the step on the wheel increases as the wheel ascends By conservation of angular momentum about point of contact: Li=LF⇒(mv)R2+Icmω0=2mR2ω…(1) For rolling , ω0=vR : So, eqn-(i) becomes →12mvR+12mR2(vR)=2mR2c⇒[ω=3v4R]. At time of contact : As it ascends, θ decrease ⇒cosθ increases so, N increases as wheel ascents. Option A and C are correct.

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