Question

A steel ball of 10 m radius was subjected to uniform pressure of 10 MPa. Using typical materials properties for steel the change of the mass can be estimated (in kg) as

a 0
b -20
c 2
d 0.0134
e -0.0134
f -2
g 20

Answer 1

The change in mass of the steel ball can be estimated using the formula: Δm = V · ΔP / B. In this case, the ball is subjected to a uniform pressure of 10 MPa, and we can use the properties of typical steel to calculate the change in mass. The estimated change in mass of the steel ball is approximately 0.01995 kg.

Step-by-step explanation:

The change in mass of the steel ball can be estimated using the formula:

Δm = V · ΔP / B

Where Δm is the change in mass, V is the volume of the ball, ΔP is the change in pressure, and B is the bulk modulus of the material. In this case, the ball is subjected to a uniform pressure of 10 MPa, and we can use the properties of typical steel to calculate the change in mass.

Given that the radius of the ball is 10 m, the volume can be calculated as:

V = (4/3)πr³ = (4/3)π(10 m)³ = 4188.79 m³

Using the bulk modulus of steel as 210 × 10⁹ N/m², the change in mass can be calculated as:

Δm = (4188.79 m³)(10 MPa) / (210 × 10⁹ N/m²) = 0.01995 kg

Therefore, the estimated change in mass of the steel ball is approximately 0.01995 kg.