The following figure shows two situations in which a uniform round rigid body is released from rest from the positions shown, such that it is just able to loop the loop without leaving contact with the track. Assuming that radius of the track is large in comparison to the radius of round body, the ratio h1 / h2.

Engineering

Physics

Rolling

Question

The following figure shows two situations in which a uniform round rigid body is released from rest from the positions shown, such that it is just able to loop the loop without leaving contact with the track. Assuming that radius of the track is large in comparison to the radius of round body, the ratio h₁ / h₂.

can be greater than or less than 1, depending on the moment of inertia of the round body.

must be less than 1

must be equal to 1

must be greater than 1

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Case-1 : mg h₁ = (K.E.)_translation = K_trans. $= \frac{1}{2} {mv}^{2}$
Whole gravitational potential energy is converted into translational K.E. only
Case-2 : mgh₂ = K_trans + K_rot $= \frac{1}{2} {mv}^{2} + \frac{1}{2} I_{cm} ω^{2}$
Some part of gravitational potential energy will be converted into rotational K.E. also.
Hence in second case, greater height is required.

Please subscribe our Youtube channel to unlock this solution.