An adult elephant has a mass of about 5.0 tons. An adult elephant shrew has a mass of about 50 grams. How far r from the center
1 answer:
Answer:
2023857702.507 m
Explanation:
Using Newton's law of gravitation:
G = gravitational constant
m_shrew = 50 g
m_elephant = 5 × 10^3 kg
r_earth = Earth's radius, 6400 km or 6,400,000 m
m_earth = Earth's mass
Equate the gravitational forces:
G m_shrew m_earth / r_earth^2 = G m_elephant m_earth / r^2
Cancel common terms on both sides:
m_shrew / r_earth^2 = m_elephant / r^2
Rearranged to solve for r^2:
r^2 = (m_elephant × r_earth^2) / m_shrew
Substituting the values:
r^2 = 4.096 × 10^{13}
Taking square root gives:
r = 2,023,857,702.507 m
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Response:
Clarification:
Refer to the diagram indicating the charges on the specified sphere (see attachment).
The electric field at the stated positions is
E(r) = 0 for r≤a. Equation 1
E(r) = kq/r² for a<r<b. Equation 2
E(r) = 0 for b<r<c. Equation 3
E(r) = kq/r² for r>c. Equation 4.
We understand that electric potential correlates with the electric field through
V = Ed
A. To compute the potential at the outer surface of the hollow sphere (r=c), we determine that the electric field there is
E = kQ / r²
Then,
V = Ed,
At d = r = c
Thus,
Vc = (kQ / c²) × c
Vc = kQ / c
As a result, the total charge Q consists of +q, -q, and +q
Hence, Q = q - q + q = q
V = kq / c
B. To calculate the potential at the inner surface of the hollow sphere (r=b), we have
V = kQ/r
V = kQ / b, noting that r = b
So, Q = q
V = kq / b
C. At r = a
Following from equation 1:
E(r) = 0 for r≤a. Equation 1
The electric field at the surface of the solid sphere is 0, E = 0N/C
Thus,
V = Ed = 0 V
Consequently, the electric potential at the solid sphere's surface is 0.
D. At r = 0
The electric potential can be determined by
V = kq / r
As r approaches 0,
V = kq / 0
V approaches infinity.
