Which of the points is the likely position of the centre of mass of the system shown in the figure?

Two point masses $m$ and $M$ are separated by a distance $L$. The distance of the centre of mass of the system from $m$ is

If the linear mass density of a rod of length $L$ varies as $\lambda = kx^3$,determine the position of its centre of mass (where $x$ is the distance from one of its ends and $k$ is a constant):

If the linear density of a rod of length $3 \ m$ varies as $\lambda = 2 + x$,then the position of the centre of mass of the rod is:

$A$ uniform rod of length $L$ and mass $M$ is placed along the $x$-axis with its one end at the origin. The centre of mass of the rod is located at:

$A$ uniform thin rod $AB$ of length $L$ has linear mass density $\mu(x) = a + \frac{bx}{L}$,where $x$ is measured from $A$. If the $CM$ of the rod lies at a distance of $\frac{7}{12}L$ from $A$,then $a$ and $b$ are related as