Embibe Experts Solutions for Exercise 1: EXERCISE 6.1

A system consists of $3$ particles each of mass $\mathrm{m}$, located at $\left(1,1\right) \left(2,2\right)$ and $\left(3,3\right)$ respectively. The co-ordinates of the centre of mass of system are

If you have eight one kilogram blocks, how many different combinations are possible so that the centre of mass comes to the centre of the square $ABCD$. All blocks have to be used in each combination. The blocks can be kept only at the comers of the square.

The motion of the centre of mass of system of two particles is NOT affected by the internal forces

Two bodies $A$ and $B$ are attracted towards each other (beginning at rest) due to gravitation. Given that $A$ is much heavier than $B$, which of the following correctly describes the motion of the centre of mass of the bodies?

Two particles $A$ and $B$ of equal mass are projected simultaneously with speed $10 \mathrm{m} {\mathrm{s}}^{-1}$ each as shown in figure. Find the co-ordinate of COM at $t=10 \mathrm{s}$. (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-1}$)

Two masses $m_1=4\mathrm{kg}$ and $m_2=2\mathrm{kg}$ are released from rest as shown in figure. 

Find the distance $\left(\mathrm{in} \mathrm{m}\right)$  travelled by centre of mass in $9 \mathrm{s}$.

Two masses $m_1=4\mathrm{kg}$ and $m_2=2\mathrm{kg}$ are released from rest as shown in figure. Find the speed of the centre of mass after $9 \mathrm{s}$ in $\mathrm{m} {\mathrm{s}}^{-1}$.