Question

two brass spheres of radii 5cm and 10cm are brought in contact with each other.find the centre of gravity of the combination

Answer 1

Answer:

Since we are trying to find the center of gravity assume a constant density ρ — we can treat it as if we had the mass of each sphere based at a point at their center. It means we have the mass of the radius 3 cm sphere at a point, let's call the location d=0. Now, since we are trying to get the distance from the point. The mass of the radius 5 cm sphere is at a point d = 3cm + 5cm. That is, 8cm away. The CoM formula is - dCoM = m3d3+m5d5m3+m5 = 43π33⋅ρ⋅0+43π53⋅ρ⋅843π33⋅ρ+43π53⋅ρ = 33⋅0+53⋅833+53 = 1000152 = It is about 6.6cm from the center of the radius which of the 3cm sphere.