Two blocks of masses 10 kg and 20 kg are located on the X -axis. The first mass is displaced along the axis by a distance of 2 cm . By what distance must the second mass be moved in order to keep the position of the centre of mass unchanged?

Step-by-step solution

The position of the centre of mass of a two-particle system is given by X_ cm = m₁ x₁ + m₂ x₂ m₁ + m₂ For the centre of mass to remain unchanged, the change in its position must be zero, so X_ cm = 0 . X_ cm = m₁ x₁ + m₂ x₂ m₁ + m₂ = 0 m₁ x₁ + m₂ x₂ = 0 Substituting the given values, m₁ = 10 kg , x₁ = 2 cm , and m₂ = 20 kg : 10 2 + 20 x₂ = 0 20 + 20 x₂ = 0 x₂ = -1 cm The negative sign indicates that the second mass must be moved in the opposite direction. The distance it must be moved is 1 cm .