Question

A system consists of mass $M$ and $m$. The centre of mass of the system is:

• A. nearer to $m$.
• B. at the position of large mass.
• C. nearer to $M$.
• D. at the middle.

Answer 1

The correct option is C nearer to $M$.

Consider a system made up of two particles whose mass are $M$ and $m$ and their respective position vectors with respect to origin O be $r_1$ and $r_2$ and $R$ be the position vector of center of mass of the system.

Let, $M^{\prime }=M+m$ and $M>m$

The position of center of mass for two particle system is given by
$M^{\prime }R=M{r}_1+m{r}_2$

By definition, $M^{\prime }R=0$

Hence, $M{r}_1=-m{r}_2$

negative sign indicates that masses are present on either sides of center of mass.

Since, $M>m$, center of mass will be located nearer to M.