Question
Class 11PhysicsGravitation

An apple of mass 0.25 kg falls from a tree. What is the acceleration of the apple towards the Earth? Also calculate the acceleration of the Earth towards the apple. Given: Mass of Earth = 5.983 × 1024 kg, Radius of Earth = R = 6.378 × 106 metre, G = 6.67 × 10-11 N m2 kg-2.

 

Verified Answer

Given:

  • Mass of apple, m = 0.25 kg
  • Mass of Earth, M = 5.983 × 10²⁴ kg
  • Radius of Earth, R = 6.378 × 10⁶ m
  • Gravitational constant, G = 6.67 × 10⁻¹¹ N·m²·kg⁻²

Gravitational force between apple and Earth:

F = (GmM) / R²

Acceleration of apple towards Earth:

a = F / m = (GM) / R²

a = (6.67 × 10⁻¹¹ × 5.983 × 10²⁴) / (6.378 × 10⁶)² = 9.81 m/s²

Acceleration of Earth towards apple:

a′ = F / M = (Gm) / R²

a′ = (6.67 × 10⁻¹¹ × 0.25) / (6.378 × 10⁶)² = 4.099 × 10⁻²⁵ m/s²