Solution

**Step 1: Given**

The mass of the earth is times the mass of the moon.

The distance between the earth and the moon is times the radius of the earth ( ).

**Step 2: Formula used**

Let the mass of the moon be then the mass of the earth will be .

Formula: The gravitational force due to a body of mass on an object of mass will be , where is the gravitational constant and is the distance between the two objects.

**Step 3: Solution**

Gravitational force is a vector quantity, The force of attraction is towards the object in the line that joins the two objects.

Let the required point be at a distance from the moon.

The force from both moon and earth has to be equal at this point to make the net force zero at that specific point as they both act in opposite directions.

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T**he distance from the moon where the force due to both moon and earth will become zero is ****.**

**Step 1: Given**

The mass of the earth is

The distance between the earth and the moon is

**Step 2: Formula used**

Let the mass of the moon be

Formula: The gravitational force due to a body of mass

**Step 3: Solution**

Gravitational force is a vector quantity, The force of attraction is towards the object in the line that joins the two objects.

Let the required point be at a distance

The force from both moon and earth has to be equal at this point to make the net force zero at that specific point as they both act in opposite directions.

⇒

⇒

⇒

⇒

⇒

T**he distance from the moon where the force due to both moon and earth will become zero is ****.**