Gravitation — Important Questions

Mass of the Earth, Radius of the Earth, Rotation of the Earth, Latitude, Shape of the Earth

Acceleration due to gravity g = GM/R² depends on Earth's mass M and radius R. Earth's rotation causes centrifugal effect reducing apparent g. Latitude affects g due to rotation and Earth's oblate shape. The mass of the object cancels out in the acceleration formula, so it doesn't affect g.

R (one Earth radius)

Step-by-step solution: At height h: gₕ = GM/(R+h)² At surface: g = GM/R² Given: gₕ = g/4 Therefore: GM/(R+h)² = (1/4) × GM/R² (R+h)² = 4R² R+h = 2R h = R So at height equal to Earth's radius, gravity becomes one-fourth.

They orbit Earth in 24 hours

Geostationary satellites have an orbital period of 24 hours, which matches Earth's rotational period. This makes them appear stationary relative to Earth's surface. They orbit in the equatorial plane at a specific altitude of about 36,000 km above Earth's surface.

25 N

Step-by-step solution: Gravitational force F = Gm₁m₂/r² Initially: F₁ = 100 N at r₁ = 10 m Finally: r₂ = 2r₁ = 20 m F₂ = Gm₁m₂/(2r₁)² = Gm₁m₂/(4r₁²) = F₁/4 = 100/4 = 25 N When distance doubles, force becomes one-fourth due to inverse square law.