TS EAMCET · Physics · Laws of Motion

An iron rod of length \(1.5 \mathrm{~m}\) lying on a horizontal table is pulled up form one end along a vertical line so as to move it with a constant velocity \(3 \mathrm{~m} / \mathrm{s}\), while the other end of the rod slides along the floor. After how much time the speed of the end sliding on the floor equals to the speed of the end being pulled up.

A \(\frac{1}{2 \sqrt{2}} \mathrm{~s}\)
B \(\frac{1}{{2}} \mathrm{~s}\)
C \(3 \sqrt{2} \mathrm{~s}\)
D \(\frac{1}{4} \mathrm{~s}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{{2}} \mathrm{~s}\)

Step-by-step Solution

Detailed explanation

According to question. Given, \(A B\) is an iron rod whose length is given by \( l=1.5 \mathrm{~m} \) velocity of end \(\mathrm{A}\), \( v=3 \mathrm{~m} / \mathrm{s} \) Let \(t\) be the time when both the ends have same speed. Since, end \(A\) has always a constant 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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