Question

A block of mass '$m$' is pulled by a uniform chain of mass '$m$' tied to it by applying a force '$F$' at the other end of the chain. The tension at a point, which is at a distance of quarter of the length of the chain from the free end, will be:

• A. $\frac{3F}{4}$
• B. $\frac{7F}{8}$
• C. $\frac{6F}{7}$
• D. $\frac{4F}{5}$

Answer 1

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

If $a$ be the acceleration of the system, then:

$(m+m)a=F$

or, $a=\frac{F}{2m}$

Now T is the required tension due to mass $m_r=m+(m-\frac{m}{4})=m+\frac{3m}{4}=\frac{7m}{4}$
So, $T=m_{r}a=\frac{7m}{4}\times \frac{F}{2m}=\frac{7F}{8}$