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 distant quarter of the length of the chain from free end will be

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

Answer 1

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

If a be the acceleration of the whole system of mass $M_T=(M+M)=2M$, then $M_{T}a=F,a=\frac{F}{2M}$
acceleration a should be same where we will found tension($T$).
Now tension due to rest of mass, $m_r=M+(M-\frac{M}{4})=M+\frac{3M}{4}=\frac{7M}{4}$,
$T=m_{r}a=\frac{7M}{4}\frac{F}{2M}=\frac{7F}{8}$