Two blocks of masses 10kg and 30kg are placed on x-axis. The first mass is moved on the axis by a distance of 2cm right. By what distance should the second mass be moved to keep the position of centre of mass unchanged.

Two blocks of masses 10kg and 30kg are placed on x-axis. The first mas

1.	Two blocks of masses 10kg and 30kg are placed on x-axis. The first mass is moved on the axis by a distance of 2cm right. By what distance should the second mass be moved to keep the position of centre of mass unchanged.
Answer» Solution :mass of the first block, `m_(1)=10kg` mass of the second block, `m_(2)=30kg` Let `x_(1)` and `x_(1).` are POSITIONS of `m_(1)` `x_(2)` and `x_(1).` are positions of `m_(2)` initially and later respectively In this case if `x_(cm)` is the position of centre of mass then `x_(cm)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))` then the new position of CM when blocks are shifted `x_(cm).=(m_(1)x_(1).+m_(2)x_(2))/(m_(1)+m_(2))` subtracting the above equations `x_(cm).-x_(cm)=(m_(1)(x_(1).-x_(1))+m_(2)(x_(2).-x_(2)))/(m_(1)+m_(2))` `Deltax_(cm)=(m_(1)Deltax_(1)+m_(2)Deltax_(2))/(m_(1)+m_(2))` `0=(10xx2+30Deltax_(2))/(40)` `:.Deltax_(2)=-(2)/(3)` Therefore the second block should be moved LEFT through a distance `(2)/(3)cm` to keep the position of centre of mass UNCHANGED.