Q. A block of mass $m$ is resting on a smooth horizontal surface. One end of a uniform rope of mass $(m/3)$ 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) $\frac{7}{8}\ F$
Explanation
(d) The acceleration of the system is
[image:5_image260.emf]
$a = \frac{F}{m + \frac{m}{3}} = \frac{3F}{4m}$ …(i)
The tension in the middle of the rope ($i.e$., at point $A$) is
$T = \left( m + \frac{m}{6} \right)a = \frac{7m}{6} \times \frac{3F}{4m} \Rightarrow T = \frac{7F}{8}$ [Using (i)]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.