A raindrop has a mass of 5.6 × 10-7 kg and is falling near the surface of the earth. Calculate the magnitude of the gravitational force exerted (a) on the raindrop by the earth and (b) on the earth by the raindrop.

To calculate the magnitude of the gravitational force exerted on the raindrop by the Earth and vice versa, we can use Newton's law of universal gravitation. The formula for gravitational force is:

F = (G * m₁ * m₂) / r²

Where:
F is the magnitude of the gravitational force
G is the gravitational constant (approximately 6.674 × 10⁻¹¹ m³/(kg·s²))
m₁ is the mass of the raindrop
m₂ is the mass of the Earth
r is the distance between the center of the raindrop and the center of the Earth

Now let's proceed with the calculations for both scenarios:

(a) Magnitude of the gravitational force on the raindrop by the Earth:
To calculate the force exerted on the raindrop by the Earth, we need to know the mass of the Earth. The mass of the Earth is approximately 5.972 × 10²⁴ kg.

Using the given values:
m₁ (mass of the raindrop) = 5.6 × 10⁻⁷ kg
m₂ (mass of the Earth) = 5.972 × 10²⁴ kg

Now substituting these values into the formula:

F = (G * m₁ * m₂) / r²

F = (6.674 × 10⁻¹¹ m³/(kg·s²)) * (5.6 × 10⁻⁷ kg) * (5.972 × 10²⁴ kg) / r²

You need to provide the value of the distance (r) from the center of the raindrop to the center of the Earth to calculate the force accurately.

(b) Magnitude of the gravitational force on the Earth by the raindrop:
To calculate the force exerted on the Earth by the raindrop, we can use the same formula with the masses of the raindrop and Earth interchanged. So:

m₁ (mass of the raindrop) = 5.6 × 10⁻⁷ kg
m₂ (mass of the Earth) = 5.972 × 10²⁴ kg

Using the given values:

F = (G * m₁ * m₂) / r²

F = (6.674 × 10⁻¹¹ m³/(kg·s²)) * (5.972 × 10²⁴ kg) * (5.6 × 10⁻⁷ kg) / r²

Again, you need to provide the value of the distance (r) from the center of the raindrop to the center of the Earth to calculate the force accurately.