AP EAMCET · PHYSICS · Laws of Motion

A bar of mass \(m\) resting on a smooth horizontal plane starts moving due to a constant force \(F\). In the process of its rectilinear motion the angle \(\theta\) between the direction of this force and the horizontal varies as \(\theta=k x\), where \(k\) is a constant and \(x\) is the distance traversed by the bar from its initial position. The velocity \((v)\) of the bar as a function of the angle \(\theta\) is

A \(v=\sqrt{\frac{2 F \sin \theta}{m k}}\)
B \(v=\sqrt{\frac{2 F}{m k \sin \theta}}\)
C \(v=\frac{2 F \sin \theta}{m k}\)
D \(v=\frac{2 F}{m k \sin \theta}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(v=\sqrt{\frac{2 F \sin \theta}{m k}}\)

Step-by-step Solution

Detailed explanation

Component of force responsible for horizontal motion is \(F \cos \theta\). So, acceleration of bar, \(a=\frac{F \cos \theta}{m}\) As acceleration, \(a=\frac{d v}{d t}\), we have \(\Rightarrow \quad \frac{d v}{d t}=\frac{F \cos \theta}{m}\) we can also express this as,…

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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