Answer:
62.8 μC
Explanation:
Here is the complete question
The volume electric charge density of a solid sphere is given by the following equation: ρ = (0.2 mC/m⁵)r²The variable r denotes the distance from the center of the sphere, in spherical coordinates. What is the net electric charge (in μC) of the sphere if the radius of the sphere is 0.5 m?
Solution
The total charge on the sphere Q = ∫∫∫ρdV where ρ = volume charge density = 0.2r² and dV = volume element in spherical coordinates = r²sinθdθdrdΦ
So, Q = ∫∫∫ρdV
Q = ∫∫∫ρr²sinθdθdrdΦ
Q = ∫∫∫(0.2r²)r²sinθdθdrdΦ
Q = ∫∫∫0.2r⁴sinθdθdrdΦ
We integrate from r = 0 to r = 0.5 m, θ = 0 to π and Φ = 0 to 2π
So, Q = ∫∫∫0.2r⁴sinθdθdrdΦ
Q = ∫∫∫0.2r⁴[∫sinθdθ]drdΦ
Q = ∫∫0.2r⁴[-cosθ]drdΦ
Q = ∫∫0.2r⁴-[cosπ - cos0]drdΦ
Q = ∫∫∫0.2r⁴-[-1 - 1]drdΦ
Q = ∫∫0.2r⁴-[- 2]drdΦ
Q = ∫∫0.2r⁴(2)drdΦ
Q = ∫∫0.4r⁴drdΦ
Q = ∫0.4r⁴dr∫dΦ
Q = ∫0.4r⁴dr[Φ]
Q = ∫0.4r⁴dr[2π - 0]
Q = ∫0.4r⁴dr[2π]
Q = ∫0.8πr⁴dr
Q = 0.8π∫r⁴dr
Q = 0.8π[r⁵/5]
Q = 0.8π[(0.5 m)⁵/5 - (0 m)⁵/5]
Q = 0.8π[0.125 m⁵/5 - 0 m⁵/5]
Q = 0.8π[0.025 m⁵ - 0 m⁵]
Q = 0.8π[0.025 m⁵]
Q = (0.02π mC/m⁵) m⁵
Q = 0.0628 mC
Q = 0.0628 × 10⁻³ C
Q = 62.8 × 10⁻³ × 10⁻³ C
Q = 62.8 × 10⁻⁶ C
Q = 62.8 μC
Answer:
1. Molecular cloud
2. Close binary
3. Brown dwarf
4. Protostellar wind
5. Thermal pressure
6. Protostellar disk
7. Jet
8. Degeneracy pressure
Explanation:
1. The Sun formed, probably along with other stars, within a large molecular cloud.
2. A Close binary consists of two stars that orbit each other every few days.
3. A Brown dwarf is a "star" so small in mass that its core never gets hot enough to sustain nuclear fusion reactions.
4. Most of the gas remaining from the process of star formation is swept into interstellar space by a protostellar wind.
5. As a protostar's internal temperature increases, its growing thermal pressure helps slow its contraction due to gravity.
6. Planets may form within the protostellar disk that surrounds a forming star.
7. Mass can be lost through a jet of material ejected along a protostar's axis of rotation.
8. A "star" with mass below 0.08 solar mass has its gravitational contraction halted by degeneracy pressure.
Newton's second law is stated as:
F=ma,
a = (7-4)/1.5 = 2 m/s^2 (it is a deceleration due to impact with floor. And thus the ball exerts force on the floor).
Therefore,
F= 0.3*2 = 0.6 N
Given: Universal Gravitational constant = G = 6.67 x 10⁻¹¹ N m²/Kg²
Mass₁ = 70 Kg; Mass₂ = 70 Kg Radius r = 1.5 m; Force F = ?
Formula: F = Gm₁m₂/r²
F = (6.67 x 10⁻¹¹ N m²/Kg²)(70 Kg)(70 Kg)/(1.5 m)²
F = 1.45 X 10⁻⁷ N
