Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point:

Solution

Physics sir · 4 steps

Put the origin at the 1 kg mass, and then each coordinate needs only one mass.

1. Choose axes. Take the 1.0 kg mass at the right-angle corner as the origin. Then the 1.5 kg mass is at (3, 0) cm and the 2.5 kg mass is at (0, 4) cm. The total mass is 1.0 + 1.5 + 2.5 = 5.0 kg.

   x_(cm) = (Σ mᵢ xᵢ)/(Σ mᵢ), y_(cm) = (Σ mᵢ yᵢ)/(Σ mᵢ)

2. Horizontal position. Only the 1.5 kg mass lies off the vertical axis. So x_(cm) = (1.5 × 3)/5.0 = 4.5/5.0 = 0.9 cm.
3. Vertical position. Only the 2.5 kg mass lies above the base. So y_(cm) = (2.5 × 4)/5.0 = 10/5.0 = 2.0 cm.
4. So. The centre of mass is 0.9 cm to the right and 2.0 cm above the 1 kg mass, which is option (b).

The idea to keep. Place the origin on a mass that sits at a corner, with the axes along the sides. Masses on an axis then drop out of the other coordinate, and the arithmetic becomes very short.

Answer from the NTA final answer key. Solution by PrepWiser.