Two blocks of masses 10 kg and 30 kg are situated along a vertical line. The first block is elevated by 7 cm . By what distance must the second block be displaced in order to raise the centre of mass by 1 cm ?

Step-by-step solution

The displacement of the centre of mass of a two-particle system is given by the formula: y_ cm = m₁ y₁ + m₂ y₂ m₁ + m₂ Given m₁ = 10 kg , m₂ = 30 kg , y₁ = 7 cm (upward), and y_ cm = 1 cm (upward). Substituting the values into the formula: 1 = 10 7 + 30 y₂ 10 + 30 1 = 70 + 30 y₂ 40 40 = 70 + 30 y₂ 30 y₂ = -30 y₂ = -1 cm The negative sign indicates that the displacement is in the downward direction. Thus, the second block must be displaced by 1 cm downward.