Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

question 2 (1 point) if the moon had more mass, what would happen to lu…

Question

question 2 (1 point)
if the moon had more mass, what would happen to lunar tides?
the tides would become larger.
the tides would be less frequent because the moon would slow down.
the tides would become smaller because the moon would be smaller.
the tides would be more frequent because the moon would speed up.
nothing because the tide is caused by the moons orbital motion.

Explanation:

Brief Explanations

Tides are caused by the gravitational pull of the Moon (and the Sun). According to Newton's law of universal gravitation \(F = G\frac{m_1m_2}{r^{2}}\), where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of two objects, and \(r\) is the distance between their centers. If the mass of the Moon (\(m_1\)) increases, the gravitational force it exerts on the Earth (and the water on Earth's surface) will increase. A stronger gravitational pull from the Moon would lead to larger tidal bulges, meaning larger tides.
The frequency of tides is mainly related to the Moon's orbital period around the Earth (about 27.3 days for its sidereal period and about 29.5 days for its synodic period which is relevant for tidal cycles as it relates to the Earth - Moon - Sun system). An increase in the Moon's mass does not directly affect its orbital period in a way that would make tides less or more frequent. Also, an increase in mass does not imply the Moon would be smaller. And tides are not "nothing" related to the Moon's mass as the gravitational force (which depends on mass) is a key factor in tide - generation.

Answer:

The tides would become larger.