Masses $m \left(\frac{1}{3}\right)^N \frac{1}{N}$ are placed at $x=N$,where $N=2, 3, 4, \ldots \infty$. If the total mass of the system is $M$,then the centre of mass is

On a horizontal frictionless frozen lake,a girl of mass $36 \,kg$ and a box of mass $9 \,kg$ 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?

When two masses $m$ and $M$ $(M > m)$ are connected,where will the center of mass be located?

Where will the centre of mass be located when combining two masses $m$ and $M$ $(M > m)$?

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

$A$ particle of mass $m$ is moving in the $xy$-plane at a certain height from the ground along the $x$-axis. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. At that instant,the smaller fragment is at $y = 15 \ cm$. At this instant,the larger fragment will be at $y = $ ........ $cm$.