Q. 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) $\frac{8}{6}F$
B) $\frac{1}{7}F$
C) $\frac{1}{8}F$
D) $\frac{7}{8}F$
Explanation
(d) Acceleration of the system
$a = \frac{F}{\left( m + \frac{m}{3} \right)}$
$\therefore$ Tension in the middle of the rope
$T = \left( m + \frac{m}{6} \right)a$
$or\ \ T = \frac{7m}{6} \bullet \frac{3F}{4m}$
$= \frac{7}{8}F$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.