Two uniform plates of the same thickness and area but of different materials, one shaped like an isosceles triangle and the other shaped like a rectangle are joined together to form a composite body as shown in the figure alongside.If the centre of mass of the composite body is located at the mid-point of their common side, then the ratio between masses of the triangle to that of the rectangle is

The variation of density of a cylindrical thick and long rod, is $\rho  = {\rho _0}\frac{{{x^2}}}{{{L^2}}}$ , then position of its centre of mass from $x = 0$ end is

Mention the position of centre of mass of particles of equal mass. 

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

$Assertion$ : The position of centre of mass of a body depends upon shape and size of the body.
$Reason$ : Centre of mass of a body lies always at the centre of the body.

Three identical spheres each of mass $M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $3\,m$ each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $\sqrt{x} m$. The value of $x$ is