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  4. Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 15 kg 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:

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Q. Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. $A \,15\, kg$ 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:

Laws of Motion

Solution:

When a string is fixed horizontally (by clamping its free ends) and loaded at the middle, then for the equilibrium of point $P$
image
$2T\,sin\,\theta=W$ i.e., $T=\frac{W}{2\,sin\,\theta}$
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