COMEDK · Physics · 3. Motion In One Dimension

An object is dropped from a certain point A at a height 'h' from the ground. During it's journey straight downwards, the object passes points B and C such that the ratio of time taken \(t_1\) to cover AB and \(t_2\) to cover BC is 1: \((\sqrt{2} - 1)\). What is the ratio of distances AB:BC ?

A \(1:\sqrt{2}\)
B \(\sqrt{2}:1\)
C \(1:1\)
D \((\sqrt{2} - 1):1\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1:1\)

Step-by-step Solution

Detailed explanation

Let the time taken to travel from A to B be \(t_1 = t\). The time taken to travel from B to C is \(t_2 = (\sqrt{2} - 1)t\). The total time taken to travel from A to C is \(t_{AC} = t_1 + t_2 = t + (\sqrt{2} - 1)t = \sqrt{2}t\). Since the object is dropped from rest at A, the…

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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