Question

A block of mass $m$ is resting on a smooth horizontal surface. One end of a uniform rope of mass $\left(m/3\right)$ is fixed to the block, which is pulled in the horizontal direction by applying a 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. $\frac{7}{8}F$

Answer 1

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

Common acceleration
$a_{net}=\frac{F}{m+m/3}=\frac{3F}{4m}$

FBD of the right half-length of the rope

$F-T=\frac{m}{6}{a}_{net}$
or $F-T=\frac{m}{6}\times \frac{3F}{4m}$
or $T=\frac{7F}{8}$