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Comprehensive Master Sheet: Gravitation
Student Name: ____________________________________
Class: 11th (CBSE/NEET/JEE)
Subject: Physics
Section A: Variation of $g$ & Gravitational Field
1.
Derive variation of acceleration due to gravity $g$ with height $h$ ($g' = g(1 - 2h/R)$) and depth $d$ ($g' = g(1 - d/R)$).
2.
At what height above Earth's surface does acceleration due to gravity become $25\%$ of its value on the surface? ($R = 6400\text{ km}$).
Section B: Escape & Orbital Velocity
3.
Derive the expression for escape velocity $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$ from Earth's surface and calculate its numerical value.
4.
A satellite orbits Earth at a height $h = R$ above the surface. Find orbital speed $v_o$ and time period $T$.
Section C: Kepler's Laws & Energy
5.
State Kepler's Three Laws of Planetary Motion and prove Kepler's 2nd law (conservation of angular momentum).
6.
Find binding energy of a satellite of mass $m$ orbiting Earth (mass $M$, radius $R$) at altitude $h$.
