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

Question

2 months ago

12

of the Earth should an elephant be placed so that its weight equals that of the elephant shrew on the surface of the Earth

1 answer:

Maru [3.3K] · Answer 1 · 2026-02-18T00:08:20+03:00

Answer:

2023857702.507 m

Explanation:

$f=\frac{GMm}{r^{2} }$

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