A body of mass M is hanging by an inextensible string of mass m. If the free end of the string accelerates up with constant acceleration a. find the variation of tension in the string a fuction of the distance measured from the mass M (bottom of the string).

Explanation

Let T be the tension in the string at a distance x from its bottom. Referring to the FBD, we have the following equations:
Force equation for `(m_1)`:
`T=m_(1)g-Mg=(M+m_(1))a` …(i)
We are writing equation of motion for lower parts as we are not given the force acting on top of the string.
Substituting `m_(1)=(m)/(l)x` in equation (i), we have
`T=(M+(mx)/(l))(g+a)`
At `x=l, T=(M+m)(g+a)=F(say)`