Question

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$\underline{\underline{\huge{ \red{\sf Question:-}}}}$


An apple of mass 0.15kg falls from a tree. What is the acceleration of the apple towards of the earth? Also calculate the acceleration of the earth towards the apple

$\sf \bigg[Given: \: Mass \: of \: each \: of \: earth \: =6×10^24 Kg$

And Radius of earth =6.4×10^6m, G=6.67Nm^2 Kg^-2]​​​

Answer 1

Explanation:

given :

• apple of mass = 0.15kg

• earth of mass = 6 x 10 kg

• earth radius = 6.4 x 10 m

• gravity constant = 6.67 x 10 Nm² kg-²

to find :

• apple of earth Acceleration = ?

• apple of earth Acceleration = ?

formula of acceleration is:

• g = GM/r²

solution :

• please check the attached file

thus :

• the acceleration of apple = 2.5 ×10 m/s

Answer 2

Answer :-

Required acceleration :-

→ Apple towrads Earth = 9.8 m/s²

→ Earth towards Apple = 2.4 × 10⁻²⁵ m/s²

Explanation :-

We have :-

• Mass of the apple (Mₐ) = 0.15 kg

• Mass of earth (Mₑ) = 6.4 × 10²⁴ kg

• Radius of earth (Mₚ) = 6.4 × 10⁶ m

• Value of "G" = 6.67 × 10⁻¹¹ Nm²/kg²

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Acceleration of apple towards earth :-

We already have a formula to calculate acceleration due to gravity for any mass and radius. So putting values, we will get the acceleration of the apple towards earth.

⇒ gₑ = GMₑ/R²ₑ

⇒ gₑ = (6.67 × 10⁻¹¹ × 6 × 10²⁴)/(6.4 × 10⁶)²

⇒ gₑ = (40.02/40.96) × 10⁻¹¹⁺²⁴⁻¹²

⇒ gₑ = 0.98 × 10

⇒ gₑ = 9.8 m/s²

Acceleration of earth towards apple :-

Just we have to replace mass of earth with mass of the apple to get required answer in this case .

⇒ gₐ = GMₐ/R²ₑ

⇒ gₐ = (6.67 × 10⁻¹¹ × 0.15)/(6.4 × 10⁶)²

⇒ gₐ ≈ (1/40.96) × 10⁻¹¹⁻¹²

⇒ gₐ ≈ 0.024 × 10⁻²³

⇒ gₐ ≈ 2.4 × 10⁻²⁵ m/s²