Four particles of masses $m_1 = 2m$,$m_2 = 4m$,$m_3 = m$,and $m_4$ are placed at the four corners of a square. What should be the value of $m_4$ so that the centre of mass of all the four particles is exactly at the centre of the square?

$A$ square plate and a circular disc of uniform density are arranged as shown in the figure. The center of mass of this combined system will be .........

$A$ ladder is leaning against a smooth wall and is free to slide on a frictionless floor. Which of the following diagrams correctly represents the path of the center of mass of the ladder?

An isolated particle of mass $m$ is moving in a horizontal $x-y$ plane along the $x-$axis at a certain height above the ground. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. An instant later,the smaller fragment is at $y = 15 \ cm$. The larger fragment at this instant is at $y = \dots \ cm$.

In the case of a system of two particles of different masses,the centre of mass lies

The coordinates of the center of mass of the triangular lamina shown in the figure are ....... .