JEE Main · PhysicsHard
A particle is dropped from a height $h$ above the surface of the earth. If the time taken to reach the surface is $t$, what is the expression for $t$ considering the variation of gravity with height $g(r) = \frac{GM}{r^2}$?
- A.$\sqrt{\frac{2h}{g}}$
- B.$\sqrt{\frac{h}{g}}(1 + \frac{h}{4R})$
- C.$\sqrt{\frac{2h}{g}}(1 + \frac{h}{6R})$
- D.$\sqrt{\frac{2h}{g}}(1 + \frac{h}{3R})$
Show correct answer & step-by-step solution
Correct answer: C — $\sqrt{\frac{2h}{g}}(1 + \frac{h}{6R})$
Solution
Integrating from to . Using and binomial expansion for , the integral yields .
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