Question

The gravitational force between two identical spheres kept at 2m apart is 0.007784N.Find their masses​

Answer 1

Answer:-

21610.18 kg

Explanation:-

Since the two spheres are identical, thus their masses will be equal.

Let the mass of the spheres be 'm' kg.

We can write the gravitational force between the spheres as :-

=> 0.007784 = 7.784/1000

=> 7.784×10⁻³ N

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Now, according to Newton's Universal Law of Gravitation, we know that :-

F = GMm/r²

Where :-

• F is gravitational force between.

• G is Universal Gravitational Constant.

• M is mass of the 1st body.

• m is mass of the 2nd body.

• r is the distance between the bodies.

→ Value of 'G' = 6.67×10⁻¹¹ Nm²/kg²

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Substituting values, we get :-

=> 7.784×10⁻³ = 6.67×10⁻¹¹×m×m/(2)²

=> 7.784×10⁻³ = 6.67×10⁻¹¹m²/4

=> 7.784×10⁻³ = 1.6675×10⁻¹¹m²

=> m² = 7.784×10⁻³/1.6675×10⁻¹¹

=> m² = 4.67×10⁸

=> m² = 467000000

=> m = √467000000

=> m = 21610.18 kg

Thus, masses of the spheres are 210610.18 kg.