Question

A platinum sphere with radius 0.0119 0.0119 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× 10 4 2.14×104 kg/m3 and 1.36× 10 4 1.36×104 kg/m3, respectively.

weight?

buoyant force?

apparent weight?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of platinum = ₁ = 21400 kg/m³

Density of mercury = ₂ = 13600 kg/m³

Radius of the platinum sphere = R = 0.0119 m

Volume of the sphere = V

V = 4R³/3

V = 4(0.0119)³/3

V = 7.059 x 10^-6 m³

Weight of the platinum sphere = W

W = ₁Vg

W = (21400)(7.059x10^-6)(9.81)

W = 1.482 N

Buoyant force on the platinum sphere = F_b

F_b = ₂Vg

F₂ = (13600)(7.059x10^-6)(9.81)

F₂ = 0.942 N

Apparent weight of the platinum sphere in mercury = W_a

W_a = W - F_b

W_a = 1.482 - 0.942

W_a = 0.54 N

Weight of the platinum sphere = 1.482 N

Buoyant force on the platinum sphere = 0.942 N

Apparent weight of the platinum sphere in mercury = 0.54 N