A point-like object of mass m starts from point K with vertical initial speed v₀, slides along the full length of a smooth circular track of radius R in a vertical plane, then leaves the track and travels freely to point C as shown.

Physics · Work , Power and Energy · vertical circular motion

JEE Advanced

A point-like object of mass m starts from point K with vertical initial speed v₀, slides along the full length of a smooth circular track of radius R in a vertical plane, then leaves the track and travels freely to point C as shown.

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Sub-question 1

For the smooth track/projectile system shown, determine the vertical initial speed v₀ at K.

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Sub-question 2

For the same system, the minimum possible horizontal distance d=OC required for the object to traverse the entire track is:

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Sub-question 3

For the same system, the normal force at point A is:

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