TS EAMCET · Physics · Mechanical Properties of Solids

String $A B$ of unstretched length $L$ is stretched by applying a force $F$ at the mid-point $C$ such that the segments $A C$ and $B C$ make an angle $θ$ with $A B$ as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio $K$ . The force $F$ is given by

A $K L (1 - \tan θ) \sin θ$
B $2 K L (1 - \cos θ) \tan θ$
C $K L (1 - \cos θ) \tan θ$
D $2 K L (1 - sinθ) \tan θ$

Verified Solution

Answer & Solution

Correct Answer

(C) $K L (1 - \cos θ) \tan θ$

Step-by-step Solution

Detailed explanation

Refer the diagram applying Lami's thorem, Fsin180-2θ=Tsin90+θ ∴ Fsin2θ=Tcosθ⇒F2sinθcosθ=Tcosθ ∴ F=2sinθ×T ...1…

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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String A B of unstretched length L is stretched by applying a force F at the mid-point C such that the segments A C and B C make an angle θ with A B as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio K . The force F is given by

Step-by-step Solution