Question

A block of mass $m$ is resting on a smooth horizontal surface. One end of a uniform rope of mass $ \left( \frac{m}{3} \right) $ 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}{7}F $
• B. $ \frac{1}{7}F $
• C. $ \frac{1}{8}F $
• D. $ \frac{1}{5}F $
• E. $ \frac{7}{8}F $

Answer 1

Answer: (E)

Acceleration of the system
$ a=\frac{F}{\left( m+\frac{m}{3} \right)} $
$ \therefore $ Tension in the middle of the rope $ t=\left( M+\frac{M}{6} \right)a $
Or $ T=\frac{7m}{6}.\frac{3F}{4m} $
Or $ T=\frac{7}{8}F $