$A$ solid cylinder of mass $2 \ kg$,length $40 \ cm$ and radius $10 \ cm$ is placed in contact with a solid sphere of mass $0.5 \ kg$ and radius $10 \ cm$ such that the centres of the two bodies lie along the geometrical axis of the cylinder. The distance of the centre of mass of the system of two bodies from the centre of the sphere is (in $cm$)

$A$ point mass $m_A$ is connected to a point mass $m_B$ by a massless rod of length $l$ as shown in the figure. It is observed that the ratio of the moment of inertia of the system about the two axes $AA$ and $BB$,which are parallel to each other and perpendicular to the rod,is $\frac{I_{BB}}{I_{AA}} = 3$. The distance of the centre of mass of the system from the mass $m_A$ is

$A$ thin bar of length $L$ has a mass per unit length $\lambda$ that increases linearly with distance $x$ from one end. If its total mass is $M$ and its mass per unit length at the lighter end $(x=0)$ is $\lambda_0$,then the distance of the centre of mass from the lighter end is:

Masses $8\,kg, 2\,kg, 4\,kg, 2\,kg$ are placed at the corners $A, B, C, D$ respectively of a square $ABCD$ of diagonal $80\,cm$. The distance of the centre of mass from $A$ will be ........ $cm$.

Find the centre of mass of a uniform $L$-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is $3 \; kg$.

For determining the centre of mass of a body,why is a body considered as being composed of multiple small mass elements?