Gravitation

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Every body in the universe attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Formula: \…

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Given: \( m_1 = 100 \, \text{kg}, m_2 = 200 \, \text{kg}, r = 2 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{Nm}^2\text{kg}^{-2} \) Step 1: Use formula \( F = G \frac{m_1 m_2}{r^2} \) Step 2: \( F…

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Both are pulled by Earth's gravity. The apple falls straight because it has no sideways speed. The Moon has high tangential velocity, so it keeps 'falling' around Earth in orbit. This is like throwing…

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Gravitational force on mass m: \( F = G \frac{M m}{R^2} \) By Newton's second law: \( F = m g \) So, \( m g = G \frac{M m}{R^2} \) Cancel m: \( g = G \frac{M}{R^2} \) Where M = Earth's mass, R = E…

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Given: \( M = 5.97 \times 10^{24} \, \text{kg}, R = 6.37 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{Nm}^2\text{kg}^{-2} \) Formula: \( g = G \frac{M}{R^2} \) Step 1: \( R^2 = (6.37 \…

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As height (h) increases, 'g' decreases. For small h compared to R, \( g_h = g \left(1 - \frac{2h}{R}\right) \). This is because gravity weakens with square of distance from Earth's center. Example: At…

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Given: \( h = 1000 \, \text{km} = 10^6 \, \text{m}, R = 6.4 \times 10^6 \, \text{m}, g = 9.8 \, \text{ms}^{-2} \) Formula: \( g_h = \frac{g}{\left(1 + \frac{h}{R}\right)^2} \) Step 1: \( \frac{h}{R}…

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As we go deeper, only the mass below that point contributes to gravity. The outer shell exerts no net gravitational force. So, effective mass attracting decreases, reducing 'g'. At Earth's center, g =…