The value of acceleration due to gravity at Earth's surface is   9.8   m   s - 2 . The…

The value of acceleration due to gravity at Earth's surface is  9.8 m s-2 . The altitude above its surface at which the acceleration due to gravity decreases to  4.9 m s-2, is close to: (Radius of earth  =6.4×106 m )
  1. 1.6×106 m
  2. 2.6×106 m
  3. 6.4×106 m
  4. 9.0×106 m

Solution

Acceleration due to gravity g=GMR2 .......(1)
⇒g2=GM(R+h)2 ............(2)
From (1) and (2),
GM2R2=GM(R+h)2
R+h=2R
h=0.414×6.4×106
=2.6×106 m

Asked in: JEE Main 2019 (10 Apr Shift 1)

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