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

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

1.	Two blocks of masses 10 kg and 30 kg are placed on x - axis. The first mass is moved on the axis by a distance of 2 cm 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)=10` kg mass of the second block, `m_(2)=30` kg Let `x_(1)` and `x_(1)` are positions of `m_(1)` `x_(2)` and `x_(1)` are positions of `m_(2)` intially 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)-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 sccond block should be moved left`(2)/(3)` cm to KEEP the position of centre of mass unchanged.