Question

Two lead spheres each of mass 500g are kept with their centers 1m part. Find the gravitational force with which they attract each other?

Answer this question I will mark you as brilliant ​

Answer 1

Answer :

• Gravitational force of attraction between the two bodies is 16.675 × 10⁻¹⁴ N.

Explanation :

Given :

• Mass of the two spheres, m₁ = m₂ = 500 g or 0.5 kg
• Distance of seperation between them, d = 1 m.
• Universal gravitation constant, G = 6.67 × 10⁻¹¹ N m² kg⁻²

To find :

• Gravitational force of attraction between the two bodies, g = ?

Knowledge required :

Formula for Gravitational force of attraction :

$\boxed{\sf{F = G\dfrac{m_{1}m_{2}}{d^{2}}}}$

Where,

• F = Gravitational force of attraction
• m₁ = Mass of the body
• m₂ = Mass of the body
• d = Distance of seperation between the two bodies.

Solution :

By using the formula for Gravitational force of attraction and substituting the values in it, we get :

$:\implies \sf{F = G\dfrac{m_{1}m_{2}}{d^{2}}} \\ \\ :\implies \sf{F = 6.67 \times 10^{-11} \times \dfrac{0.5 \times 0.5}{1^{2}}} \\ \\ :\implies \sf{F = 6.67 \times 10^{-11} \times 0.5 \times 0.5} \\ \\ :\implies \sf{F = 6.67 \times 10^{-11} \times 0.5^{2}} \\ \\ :\implies \sf{F = 6.67 \times 10^{-11} \times 0.25} \\ \\ :\implies \sf{F = 6.67 \times 10^{-11} \times 2.5 \times 10^{-3}} \\ \\ :\implies \sf{F = 16.675 \times 10^{[-11 + (-3)]}} \\ \\ :\implies \sf{F = 16.675 \times 10^{-14}} \\ \\ \boxed{\therefore \sf{F = 16.675 \times 10^{-14}\:N}}$

Therefore,

• Gravitational force of attraction between the two bodies, F = 16.675 × 10⁻¹⁴ N.

Answer 2

$\huge{\boxed{\rm{Question}}}$

Two lead spheres each of mass 500g are kept with their centers 1 m part. Find the gravitational force with which they attract each other?

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

As we see that there are 2 spheres mass given so we have to write them as

• Mass of sphere₁ = Mass of sphere₂ = 500 grams / 0.5 kilograms.

• Separation difference between both of them ( spheres ) = 1 m

• Universal gravitational constant = 6.67 × 10-¹¹N m² kg-²

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Gravitational force between two sphere's / bodies.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Gravitational force between two sphere's / bodies = 16.675 × 10-¹⁴N

$\large{\boxed{\boxed{\sf{We \: also \: write \: these \: as}}}}$

• Gravitational constant as G.

• Distance of separation as d.

• Mass as m.

• Mass of sphere₁ as m₁

• Mass of sphere₂ as m₂

• Kilograms as kg.

• Gram as g.

• Force as F.

• Square as ²

$\large{\boxed{\boxed{\sf{Using \: formula}}}}$

• Universal law of Gravitational force ( Newton's law )

F = G (m₁ m₂) / d²

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that the two lead spheres each of mass 500 g are kept with their centers 1 m part. Means both bodies are of same mass. Afterthat it ask us to find the gravitational force with which they ( sphere's / bodies ) attract each other.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question we have to use this formula F = G (m₁ m₂) / d² afterthat using this formula we get our final result that is 16.675 × 10-¹⁴N

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

Using the formula to find Gravitational force of attraction we have to put the values.

Firstly,

• F = G (m₁ m₂) / d²

Means,

• f means force.

• m₁ means Mass of body

• m₂ means Mass of body

• d means Distance of separation

Putting the values we get

F = G (m₁ m₂) / d²

F = 6.67 × 10-¹¹ × (0.5 × 0.5) / 1²

F = 6.67 × 10-¹¹ × (0.5 × 0.5)

F = 6.67 × 10-¹¹ × 0.5²

F = 6.67 × 10-¹¹ × 0.25

F = 6.67 × 10-¹¹ × 2.5 × 10-³

F = 16.675 × 10^[-11+(-3)]

F = 16.675 × 10^[-11-3]

F = 16.675 × 10^[-14]

F = 16.675 × 10-¹⁴N