Gravitation

JEE Main level, single correct, medium

73 of 223

Question 73 of 223

The percentage decrease in the weight of a rocket, when taken to a height of 32km32km above the surface of earth will, be
(Radius of earth =6400km=6400km)

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Answer: (A) 11%

Acceleration due to gravity at a height h<<Rh\lt \lt R is
g′=g(1−2hR){g}^{'}=g\left(1-\dfrac{2h}{R}\right)
Now, change in gg is
∴Δgg=2hR∴\dfrac{\Delta g}{g}=\dfrac{2h}{R}
Percentage change is
⇒Δgg×100=2hR×100\Rightarrow \dfrac{\Delta g}{g}\times 100=\dfrac{2h}{R}\times 100
=2×326400×100=1=2\times \dfrac{32}{6400}\times 100=1%

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