Answer:
a) Option D is correct.
The center of mass between the Eartg and the moon is inside the Earth.
Explanation:
Given,
Mass of the moon = (7.35×10²²) kg
Mass of the Earth = (6.00×10²⁴) kg
Mass of the Sun = (2.00×10³⁰) kg
Distance between the Earth and the moon = (3.80×10⁵) km
Distance between the Earth and the Sun = (1.50×10⁸) km
With the assumption that all.of the bodies being considered are on the same straight line on the x-axis,
Note that Centre of mass is given as
C.M = (Σmx)/(Σm)
For the Earth-moon system, let the earth be x=0, then the moon is at x = (3.80 × 10 5) km away.
C.M = (Σmx)/(Σm)
Σmx = (6.00×10²⁴)) × (0) + (7.35×10²²) × (3.80×10⁵) = (2.793 × 10²⁸) kg.km
Σm = (6.00×10²⁴) + (7.35×10²²) = (6.0735 × 10²⁴) kg
CM = (2.793 × 10²⁸) ÷ (6.0735 × 10²⁴)
CM = (4.60 × 10³) km = 4600 km
This means the centre of mass is 4600 km from the Earth.
The Earth's radius = 6378 km
Hence, the centre if mass is inside the Earth.
Hope this Helps!!!
