AP EAMCET · PHYSICS · Laws of Motion

As shown in the figure, two particles, each of mass $' m'$ tied at the ends of a light string of length $2 a$ are kept on a frictionless horizontal surface. When the mid point $(P)$ of the string is pulled vertically upwards with a small but constant force $F,$ the particles move towards each other on the surface. Magnitude of acceleration of each particle, when the separation between them becomes $2 x$ is

A $\frac{F}{2 m} \frac{a}{\sqrt{a^{2} - x^{2}}}$
B $\frac{F}{2 m} \frac{x}{\sqrt{a^{2} - x^{2}}}$
C $\frac{F}{2 m} \frac{x}{a}$
D $\frac{F}{2 m} \frac{\sqrt{a^{2} - x^{2}}}{x}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{F}{2 m} \frac{x}{\sqrt{a^{2} - x^{2}}}$

Step-by-step Solution

Detailed explanation

From the above diagram,tanθ=a2-x2x, 2Tsinθ=F and Tcosθ=mafrom the above equations,a=Fcotθ2m⇒a=F2m1tanθ=F2mxa2-x2

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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