D. Most rocks are a mixture of minerals. They can vary on the types of minerals, like crystals.
Answer:
Part a)
Work done is given as
W = -121.5 J
Part b)
Potential energy of the system is given as
Explanation:
As we know that work done by variable force is given as
here we know that
so we have
so we have
here we displace it from x = 2 to x = 5
so we will have
Part b)
As we know that change in Potential energy = work done
Answer:
Explanation:
It is given that,
Height of the building, h = 245 ft
The base of the building and shadow is x.
Let is the angle of elevation that is formed by lines from the top and bottom of the building to the tip of the shadow. Using the trigonometric ratio as :
When x = 300 feet
So, the rate of change of the angle of elevation is -0.001633 rad/ft. Hence, this is the required solution.
Answer:
a) 1.082 × 10⁻¹⁹C ( e = 1.6 × 10⁻¹⁹C)
b) 3.466 × 10¹¹ N/C
Explanation:
a)
p(r) = -A exp ( - 2r/a₀)
Q = ₀∫^∞ ₀∫^π ₀∫^2xπ p(r)dV = -A ₀∫^∞ ₀∫^π ₀∫^2π exp ( - 2r/a₀)r² sinθdrdθd∅
Q = -4πA ₀∫^∞ exp ( - 2r/a₀)r²dr = -e
now using integration by parts;
A = e / πa₀³
p(r) = - (e / πa₀³) exp (-2r/a₀)
Now Net charge inside a sphere of radius a₀ i.e Qnet is;
= e - (e / πa₀³) ₀∫^a₀ ₀∫^π ₀∫^2π r² exp (-2r/a₀)dr
= e - e + 5e exp (-2) = 1.082 × 10⁻¹⁹C ( e = 1.6 × 10⁻¹⁹C)
b)
Using Gauss's law,
E × 4πa₀ ² = Qnet / ∈₀
E = 4πa₀ ² × Qnet × 1/a₀²
E = 3.466 × 10¹¹ N/C