Unit – II C

Effect of Altitude and Depth on Acceleration Due to Gravity:

Variation of ‘g’ due to Altitude ‘h’:

  • The acceleration due to gravity on the surface of the earth is given by

Gravitation Unit 2 C 01

  • The acceleration due to gravity at height ‘h’ from the surface of the earth is given byGravitation Unit 2 C 02(Expanding binomially and h being very small compared to R, the terms of higher order of h are neglected)

Gravitation Unit 2 C 03

  • This is an expression for the acceleration due to gravity at small height ‘h’ from the surface of the earth. This expression shows acceleration due to gravity decreases as we move away from the surface of the earth.


Loss in Weight of a Body at Height ‘h’:

Gravitation Unit 2 C 04Variation of ‘g’ due to Depth ‘d’:

  • The acceleration due to gravity on the surface of the earth is given by .

Gravitation Unit 2 C 10

  • Let ‘ρ’ be the density of the material of the earth.

Gravitation Unit 2 C 05

  • Now, let the body be taken to the depth ’d’ below the surface of the earth. Then acceleration due to gravity at the depth ’d’ below the surface of the earth is given by
    Gravitation Unit 2 C 06
  • This is an expression for the acceleration due to gravity at the depth ’d’ below the surface of the earth. This expression shows
  • At the centre of the earth d = R, hence acceleration due to gravity at the centre of the earth is zero.


Relation between gd and gh

  • The acceleration due to gravity at small height h from the surface of the earth is given by

Gravitation Unit 2 C 07

  • The acceleration due to gravity at the depth ’d’ below the surface of the earth is given by

Gravitation Unit 2 C 08

  • When gh = gd, then d = 2h
  • Thus the acceleration due to gravity at small height ‘h’ from the surface of the earth is the same as the acceleration due to gravity at the depth ‘d = 2h’ below the surface of the earth.
  • It means that the value of acceleration due to gravity at small height from the surface of the earth decreases faster than the value of the acceleration due to gravity at the depth below the surface of the earth.


Variation of g with Altitude and Depth:

Gravitation Unit 2 C 09

Notes:

  • The loss in weight of the body at altitude h is given by

Gravitation Unit 2 C 11

  • The weight of body at small altitude h is given by

Gravitation Unit 2 C 12

  • If earth stops rotating about its axis i.e. ω = 0, the acceleration due to gravity will increase everywhere except at poles. On the equator, the increase will be maximum.
  • When a body of mass is moved from poles to the equator, the decrease in the weight of the body is

  • The difference between acceleration due to gravity on the poles and that on the equator is

Acceleration Due to Gravity effect of altitude depth



Acceleration Due to Gravity effect of altitude depth

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