Question

A platinum sphere with radius 0.0155 m is totally immersed in mercury. Find the weight of the sphere, the buoyant force acting on the sphere, and the sphere\'s apparent weight. The densities of platinum and mercury are 2.14 × 104 kg/m3 and 1.36 × 104 kg/m3, respectively.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of platinum = ₁ = 2.14 x 10⁴ kg/m³

Density of mercury = ₂ = 1.36 x 10⁴ kg/m³

Radius of the platinum sphere = R = 0.0155 m

Volume of the platinum sphere = V

V = 4R³/3

V = 4(0.0155)³/3

V = 1.56 x 10^-5 m³

Weight of the platinum sphere = W

W = ₁Vg

W = (2.14x10⁴)(1.56x10^-5)(9.81)

W = 3.275 N

Buoyancy force on the platinum sphere = F_b

F_b = ₂Vg

F_b = (1.36x10⁴)(1.56x10^-5)(9.81)

F_b = 2.081 N

Apparent weight of the platinum sphere in mercury = W₀

W₀ = W - F_b

W₀ = 3.275 - 2.081

W₀ = 1.194 N

a) Weight of the platinum sphere = 3.275 N

b) Buoyant force on the sphere = 2.081 N

c) Apparent weight of the sphere = 1.194 N