On a horizontal frictionless frozen lake, a girl $36 \,kg$ and a box $9 \,kg$ are connected to each other by means of a rope. Initially, they are $20 \,m$ apart. The girl exerts a horizontal force on the box, pulling it towards her. How far has the girl travelled when she meets the box?

From a circle of radius $a,$ an isosceles right angled triangle with the hypotenuse as the diameter of the circle is removed. The distance of the centre of gravity of the remaining position from the centre of the circle 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

The centre of mass of a body

There are some passengers inside $a$ stationary railway compartment. The track is frictionless. The centre of mass of the compartment itself (without the passengers) is $C_1$, while the centre of mass of the 'compartment plus passengers' system is $C_2$. If the passengers move about inside the compartment along the track.

Three identical spheres, each of mass $1\ kg$ are placed touching each other with their centres on a straight line. Their centres are marked $K, L$ and $M$ respectively. The distance of centre of mass of the system from $K$ is