Physics - NLM Question with Solution | TestHub

Mass of the block = $M$

Mass of the rope = $\frac{M}{2}$

Total mass of the system = $M+\frac{M}{2}=\frac{3M}{2}$

Acceleration of the system $a=\frac{F}{\frac{3M}{2}}=\frac{2F}{3M}$

The tension in the middle of the rope accelerates the block and the rear half of the rope.

Mass behind the middle point $m^{\prime }=M+\frac{1}{2}\left(\frac{M}{2}\right)=M+\frac{M}{4}=\frac{5M}{4}$

Tension at the middle of the rope $T=m^{\prime }a=\left(\frac{5M}{4}\right)\left(\frac{2F}{3M}\right)=\frac{5F}{6}$

Answer: $\frac{5F}{6}$