Question

A block of mass $M$ is resting on a smooth horizontal plane. One end of a uniform rope of mass $\frac{M}{4}$ 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

• A. $\frac{F}{2}$
• B. $\frac{F}{5}$
• C. $\frac{9}{10}F$
• D. $F$

Answer 1

Answer: (C)

$\frac{9}{10}F$

Answer 2

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 $T, \, FBD$ of the system Applying Newton's $2^{n d}$ law, $T=\left(M + \frac{M}{8}\right)a=\frac{9 M}{8}\times \frac{4 F}{5 M}=\frac{9}{10}F$