Question

A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass $\frac{m}{3}$ is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is:

• A. $\frac{8}{6}F$
• B. $\frac{1}{7}F$
• C. $\frac{1}{8}F$
• D. $\frac{7}{8}F$

Answer 1

The correct option is D $\frac{7}{8}F$

Acceleration to the mid rope
$a=\frac{T}{m+\frac{m}{6}}=\frac{6T}{7m}$ ($m+\frac{1}{2}rope$)
For full rope
$a=\frac{F}{\left(m+\frac{m}{3}\right)}$
$\frac{6T}{7m}=\frac{3F}{4m}$
$T=\frac{7F}{8}$