In a system two particles of masses $m_1=3 \mathrm{~kg}$ and $\mathrm{m}_2=2 \mathrm{~kg}$ are placed at certain distance from each other. The particle of mass $m_1$ is moved towards the center of mass of the system through a distance $2 \mathrm{~cm}$. In order to keep the center of mass of the system at the original position, the particle of mass $\mathrm{m}_2$ should move towards the center of mass by the distance_______.$\mathrm{cm}$.

Distance of the centre of mass of a solid uniform cone from its vertex is $z_0$ . If the radius of its base is $R$ and its height is $h$ then $z_0$ is equal to

A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of cone, the position of the centre of mass of the toy is given by

Mass is distributed uniformly over a thin square plate. If two end points of diagonal are $(-2, 0)$ and $(2, 2)$, what are the coordinates of centre of mass of plate ?

A stick has its bottom end attached to a wall by a pivot and is held up by a massless string attached to its other end. Which of the following scenarios has the smallest tension in the string ? (Length of stick is same in all scenarios)

Two particles of masses $m_1$ and $m_2$ $(m_1 > m_2)$, initially at rest, move towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass $(CM)$ of the system