Answer:
r = 4.44 m
Explanation:
For this exercise we use the Archimedes principle, which states that the buoyant force is equal to the weight of the dislodged fluid
B = ρ g V
Now let's use Newton's equilibrium relationship
B - W = 0
B = W
The weight of the system is the weight of the man and his accessories (W₁) plus the material weight of the ball (W)
σ = W / A
W = σ A
The area of a sphere is
A = 4π r²
W = W₁ + σ 4π r²
The volume of a sphere is
V = 4/3 π r³
Let's replace
ρ g 4/3 π r³ = W₁ + σ 4π r²
If we use the ideal gas equation
P V = n RT
P = ρ RT
ρ = P / RT
P / RT g 4/3 π r³ - σ 4 π r² = W₁
r² 4π (P/3RT r - σ) = W₁
Let's replace the values
r² 4π (1.01 10⁵ / (3 8.314 (70 + 273)) r - 0.060) = 13000
r² (11.81 r -0.060) = 13000 / 4pi
r² (11.81 r - 0.060) = 1034.51
As the independent term is very small we can despise it, to find the solution
r = 4.44 m
It shows the ray passing through the boundary.
B. Nancy is the tallest person in the class.
Explanation:
Mass of two soccer balls, 
Initial speed of first ball, 
Initial speed of second ball, 
After the collision,
Final speed of the second ball, 
(a) The momentum remains conserved. Using the conservation of momentum to find it as :
is the final speed of the first ball
(b) Let 
is the kinetic energy of the first ball before the collision. It is given by :
It is at rest, so, the kinetic energy of the first ball before the collision is 0.
(c) After the collision, the second ball comes to rest. So, the kinetic energy of the second ball after the collision is 0.
Hence, this is the required solution.
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