If two bodies of masses $2 \,kg$ and $3 \,kg$ are moving at right angles with velocities $20 \,m \,s^{-1}$ and $10 \,m \,s^{-1}$ respectively, then the velocity of the centre of mass of the system of the two bodies is

Masses $m, (1/2)(m/2), (1/2)^2(m/3), \dots, (1/2)^{N-1}(m/N), \dots \infty$ are placed at $x = 1, 2, 3, \dots, N, \dots \infty$ respectively. If the total mass is $M$,then the centre of mass of the system is:

On what does the position of the center of mass of a rigid body depend?

The variation of density of a solid cylindrical rod of cross-sectional area $\alpha$ and length $L$ is given by $\rho = \rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from that end $(x=0)$ is:

$A$ 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 $cm$)

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