Question

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

Answer 1

Answer:

2023857702.507m

Explanation:

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

recall from newton's law of gravitation

G=gravitational constant

mshew=50g

melephant=5*10^3kg

rearth=radius of the earth 6400km or 6400000m

mearth= masss of the earth

Gm(shrew)m(earth)/r(earth)^2 = Gm(elephant)m(earth)/r^2

strike out the left hand side and right hand side variables

m(shrew)/r(earth)^2 = m(elephant)/r^2

r^2 = m(elephant).r(earth)^2 / m(shrew)       .........make r^2 the subject of the equation

r^2=$(5*10^{3} *(6400000)^{2} )/.05$

r^2=40960000000000

r=2023857702.507m