Question

A platinum sphere with radius 0.0135 0.0135 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.

Answer 1

W=2.2 N

F=1.4 N

W'=0.8 N

Step-by-step explanation:

Given that

Radius ,r = 0.0135 m

Density of the platinum ,ρ₁ = 2.14 x 10⁴ kg/m³

Density of the mercury ,ρ₂ = 1.36 x 10⁴ kg/m³

The weight of the sphere

W= m g

mass = m = volume x density

`m=(4)/(3)\pi r^3* \rho_1\ kg`

`m=(4)/(3)* \pi* 0.0135^3* 2.14* 10^4\ kg`

m = 0.22 kg

W= 0.22 x 10 = 2.2 N (↓) ( take g =10 m/s²)

The buoyant force

`F= (4)/(3)\pi r^3* \rho_2* g`

`F=(4)/(3)* \pi* 0.0135^3* 1.36* 10^4* 10`

F= 1.4 N (↑)

The apparent weight

W' = 2.2 - 1.4 N

W'= 0.8 N