Question

Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. $A15kg$ weight is attached to the rope at the mid point which how no longer remains horizontal. The minimum tension required to completely straighten the rope is:

• A. $15kg$
• B. $15/2kg$
• C. $5kg$
• D. Infinitely large

Answer 1

Answer: (D)

When a string is fixed horizontally (by clamping its free ends) and loaded at the middle, then for the equilibrium of point $P$



$2Tsin\theta =W$ i.e., $T=\frac{W}{2sin\theta }$

Tension in the string will be maximum when $sin\theta$ is minimum i.e., $\theta =0^{\circ }$ or sin $\theta =0$ and then $T=\infty$ However, as every string can bear a maximum finite tension (lesser than breaking strength). So this situation cannot be realized practically. We conclude that a string can never remain horizontal when loaded at the middle howsoever great the tension be applied