$A$ $T$-shaped object with dimensions shown in the figure is lying on a smooth floor. $A$ force $\vec{F}$ is applied at the point $P$ parallel to $AB$,such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$.

Three particles of masses $50\, g$,$100\, g$,and $150\, g$ are placed at the vertices of an equilateral triangle of side $1\, m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be

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

Give two examples of rigid bodies whose center of mass lies outside the material of the body.

Two smooth and similar right-angled prisms are arranged on a smooth horizontal plane as shown in the figure. The lower prism has a mass $3$ times the upper prism. The prisms are held in an initial position as shown and are then released. As the upper prism touches the horizontal plane,the distance moved by the lower prism is

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. If the centre of mass of the composite body is located at the mid-point of their common side,then the ratio between the masses of the triangle to that of the rectangle is: