Question

gravitational force between two objects is 320n . calculate the gravitational force when the distance between them become 4 times??


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Answer 1

Answer:

• New gravitational force between the objects = 20 N

Explanation:

The Gravitational force between two objects is given to be 320 N Initially

Let,

Initial gravitation Force b/w objects = F₁ = 320 N

mass two objects are m₁ and m₂

distance between them is d₁

so,

→ F₁ = G m₁ m₂ / d₁²  ____equation (1)

Now, when the distance between the objects become 4 times then,

Let,

New gravitation Force b/w the bodies = F₂

mass of two objects will be same m₁ and m₂

since now distance become 4 times so, d₂ = 4 d₁

so,

→ F₂ = G m₁ m₂ / d₂²

→ F₂ = G m₁ m₂ / (4 d₁)²

→ F₂ = G m₁ m₂ / (16 d₁²)

→ F₂ = (1/16) × ( G m₁ m₂ / d₁² )

[using equation (1)]

→ F₂ = (1/16) × F₁

[putting F₁ = 320 N]

→ F₂ = 1/16 × 320

→ F₂ = 20 N

Therefore,

• New gravitational force between the objects will be 20 Newton.

Answer 2

Given :-

The Gravitational force between two objects is 320 N .

To Find:-

The Gravitational force between the objects when the distance is 4times .

Solution:-

We know that According to the law of gravitation, the force between any two objects of mass M and m is directly proportional to their masses and inversely proportional to the square of the distance between them.

so, let the distance be "R"

Now, F = $\dfrac{GMm}{R²}$ ......(i)

where,

F = Gravitational force

M = mass of the first body

m = mass of the second body

R = distance between the two objects

Now,

If the distance is 4times , then the equation would be -

F = $\dfrac{GMm}{4R²}$

Now , from the equation (i) we know the value of (F) = 320 N

Substituting its value in the above equation -

F = $\dfrac{GMm}{4R²}$

F = $\dfrac{GMm}{16R²}$

F = ( 1/ 16 ) × $\dfrac{GMm}{R²}$

F = $\dfrac{1}{16} × 320$

F = 20 N

so, The value of Gravitational force when the distance is 4times is 20N .