Question

A block is lying on a horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force $F$ at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be

• A. $F$
• B. $\frac{2F}{3}$
• C. $\frac{3F}{5}$
• D. $\frac{5F}{6}$

Answer 1

The correct option is D $\frac{5F}{6}$


Let $M$ be the mass of the block and $m$ that of the rope.
The acceleration of the block - rope system is
$a=\frac{F}{(M+m)}$
Therefore, the tension at the middle point of the rope will be
$T=(M+\frac{m}{2})a=\frac{(M+\frac{m}{2})F}{(M+m)}$
Given, $m=\frac{M}{2}$. Therefore, $T=\frac{5F}{6}$. Hence the correct choice is (d).