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

1.	Two blocks of masses 10 kg and 30 kg are placed on x - aixs. 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_(1)` and `x._(1)` are positions of `m_(2)` INITIALLY and later respectively In this case of `.x_(cm).` is the POSITION of centre 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))` `Delta x_(cm)=(m_(1)Delta x_(1)+m_(2)Delta x_(2))/(m_(1)+m_(2))` `0=(10xx2+30 Delta x_(2))/(40) "" therefore Delta x_(2)=-2//3` Therefore the second block should be moved left through a distance of 2/3 cm to keep the position of centre of mass UNCHANGED.