Question

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3. A) 37 cm B) 6.6 cm C) 79 cm D) 131 cm

Answer 1

To find the thickness of the wall of the hollow steel ball, we need to calculate the volume of the ball, weight of the water displaced, and then use the density of water to find its volume. Finally, we divide the difference in volume by the surface area of the ball to find the thickness of the wall.

Step-by-step explanation:

To find the thickness of the wall of the hollow steel ball, we can use the principle of buoyancy. When an object floats, the buoyant force acting on it is equal to the weight of the liquid it displaces. In this case, the buoyant force is equal to the weight of the water displaced by the ball.

The weight of the water displaced is equal to the weight of the entire ball (since it barely floats) minus the weight of the steel material used to make the ball.

The volume of the water displaced is equal to the volume of the ball. We can calculate the volume of the ball using its diameter and the formula for the volume of a sphere. Once we have the volume, we can find the weight of the water displaced, and then use the density of water to find its volume. Lastly, we can divide the difference in volume by the surface area of the ball to find the thickness of the wall.

Answer 2

B) 6.6 cm

Step-by-step explanation:

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3. A) 37 cm B) 6.6 cm C) 79 cm D) 131 cm

density steel 7750 to 8050 kg/m³, use 7870

density of water at 20C = 0.998 g/cm³ = 998 kg/m³

Note, the overall density must be equal to that of water, 998 kg/m³

density is the ratio of mass of a body to its volume

volume = V = ⁴/₃πr³ = ⁴/₃π(1.5)³ = 14.14 m³

Mass = 998 kg/m³ x 14.14 m³ = 14109 kg

Density of steel = 7870 kg/m³ = 14109 kg / V

V = 1.79 m³

deduct 1.79 m³ from the total volume of 14.14 m³

Volume of shell is ⁴/₃πr1³ – ⁴/₃πr2³ = ⁴/₃π(r1³ – r2³) = 1.79

divide ⁴/₃π from both sides

r1³ – r2³ = 0.428 m³

r2³ = (1.5)³ - 0.428

r2 = 1.434

to get the thickness we say that

the radius of the hollow steel ball -the radius of the ball

Thickness is 1.5 – 1.434 = 0.066 m or 6.6 cm