TS EAMCET · Physics · Motion In One Dimension

Two towns \(\mathrm{X}\) and \(\mathrm{Y}\) are connected by a regular bus service. A bus leaves in either direction at every \(t=T\) minutes. A man moving with some speed in the direction \(\mathrm{X}\) to \(\mathrm{Y}\) finds that a bus goes past him every \(t=t_1\) minutes in the direction of his motion, and every \(t=t_2\) minutes in the opposite direction. Then \(T\) is given by

A \(\frac{2 t_1 t_2}{t_1+t_2}\)
B \(\frac{\left(t_1-t_2\right) t_1}{t_1+t_2}\)
C \(\frac{2 t_2\left(t_1+t_2\right)}{\left|t_1+t_2\right|}\)
D \(\frac{t_1 t_2}{\left|t_1-t_2\right|}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{2 t_1 t_2}{t_1+t_2}\)

Step-by-step Solution

Detailed explanation

Let \(\mathrm{V}\) be the speed of bus running between towns \(\mathrm{A}\) and \(\mathrm{B}\). And, speed of the man \(=\mathrm{V}_{\mathrm{o}}\) Relative speed of the bus moving in the direction of man \(=\mathrm{V}-\mathrm{V}_{\mathrm{o}}\) As bus went pass the man every…

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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