Question

Two bodies of different mass are placed at a distance if the distance is decreased by 10% then finds the %changed in the gravitational force​

Answer 1

Answer :-

Gravitational force will increase by 19 %

Explanation :-

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Two bodies of different masses are placed at a distance , the distance is decreased by 10 %

we need to find the % changed in the gravitational force

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Let,

masses of bodies be m₁ and m₂

and initial distance between them be d

Then,

Using formula to calculate Gravitational force b/w two bodies

F = G m₁ m₂ / d²

(where F is the gravitational force applied , G is the universal gravitation constant , m₁ and m₂ are masses of objects and d is the distance b/w them)

Gravitational force (F₁) applied will be ,

→  F₁ = G m₁ m₂ / d²    ___ ①

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Now,

distance b/w bodies is decreased by 10%

so, new distance will be

→new distance = d - d×(10/100)

→new distance = d - d/10

→new distance = 9 d / 10

So,

Using formula to calculate Gravitational force between two bodies  

New gravitation force (F₂) applied will be,

→  F₂ = G m₁ m₂ / (9d/10)²

→  F₂ = G m₁ m₂ / (81 d² / 100)

→  F₂ = 100 G m₁ m₂ / (81 d²)  ___ ②

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Now,

→ (F₁ / F₂) × 100 %

→ (G m₁ m₂ / d²) / ( 100 G m₁ m₂ / (81 d²)) × 100 %

→  (81 / 100) × 100%

→ 81 %

So,

since 100 % - 81 % = 19 %

Therefore,

Gravitational force will increase by 19 % when Distance between the objects will be decreased by 10 % .

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