A block of mass M is resting on a smooth horizontal plane. One end of a uniform rope of mass M 4 is fixed to the block, which pulled it in the horizontal direction by applying a force F at the other e

Question

A block of mass M is resting on a smooth horizontal plane. One end of a uniform rope of mass M 4 is fixed to the block, which pulled it in the horizontal direction by applying a force F at the other ends. The tension in the middle of the rope is

TestHub · Accepted Answer

According to the question,

Acceleration of the system (the block and the rope),

$a = \frac{F}{M + \frac{M}{4}} = \frac{4 F}{5 M}$

Let the tension at the mid-point of the rope is $T, F B D$ of the system

Applying Newton's $2^{n d}$ law,

$T = (M + \frac{M}{8}) a = \frac{9 M}{8} \times \frac{4 F}{5 M} = \frac{9}{10} F$

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