COMEDK · Physics · 6. Work Power Energy

A motor cyclist starts from the top of an inclined plane of height h to go around a globe of death trap of radius r. The ratio of minimum height 'h' of the inclined plane to the radius 'r' of the death globe in order to go around the death globe successfully is

A \(7:2\)
B \(5:2\)
C \(3:2\)
D \(2:5\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(5:2\)

Step-by-step Solution

Detailed explanation

By conservation of mechanical energy, the velocity of the motorcyclist at the bottom of the inclined plane is given by \(mgh = \dfrac{1}{2}mv^2\) \(v = \sqrt{2gh}\) To successfully complete the vertical circular loop (globe of death) of radius \(r\), the minimum velocity…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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