Question

A thin rod of length l and mass m has a disc attached to one of its ends such that the rod and disc are coplanar. Mass of the disc is M and radius r. The distance of COM of the system from the centre of the disc is :

• A. $\frac{Ml}{2(m+M)}$
• B. $\frac{Ml}{(M+m)}$
• C. $\frac{ml}{m+M}$
• D. $\frac{ml}{2(M+m)}$

Answer 1

The correct option is D $\frac{ml}{2(M+m)}$

In the question we have to find the centre of mass of the system from the centre of the disc
Distance of Centre of Mass of the rod from the centre of the disc:$\frac{l}{2}$
Distance of centre of mass of the disc from reference point :0
According to the formula of centre of mass :
$COM={\sum }_{i=1}^{i=k}\frac{m_i{x}_i}{m_i}$
= $\frac{M\ast 0+m\ast \frac{l}{2}}{M+m}$

= $\left(\frac{m}{M+m}\right)\ast \frac{l}{2}$