CBSE Class 11-science Answered
Find the variation of acceleration due to gravity below the surface of earth at depth'd'
Asked by mz05022003 | 24 Feb, 2020, 08:13: PM
Expert Answer
Now, consider a point mass m at a depth d below the surface of the earth as shown in figure, so
that its distance from the center of the earth is ( RE − d ) as shown in the figure. The earth can
be thought of as being composed of a smaller sphere of radius (RE – d ) and a spherical shell
of thickness d. The force on m due to the outer shell of thickness d is zero.
that its distance from the center of the earth is ( RE − d ) as shown in the figure. The earth can
be thought of as being composed of a smaller sphere of radius (RE – d ) and a spherical shell
of thickness d. The force on m due to the outer shell of thickness d is zero.
As far as the smaller sphere of radius ( RE – d ) is concerned, the point mass is outside it and hence according
to the result quoted earlier, the force due to this smaller sphere is just as if the entire mass of the smaller sphere
is concentrated at the centre.
If Ms is the mass of the smaller sphere, then,
................................(1)Equation (1) is written because mass of a sphere is proportional to be cube of its radius.
Thus the force on the point mass at a depth d from earth surface is
.........................(2)Substituting for Ms from eqn.(1) , we rewrite eqn.(2) as
.........................(3)Using the definition of acceleration due to gravity g on earth surface , 
,
, we get acceleration due to gravity at a depth d from eqn.(3) as
g(d) = Force/mass = g [ 1 - ( d / RE ) ]
Thus, as we go down below earth’s surface, the acceleration due gravity decreases by a factor [ 1 - ( d / RE ) ]
Answered by Thiyagarajan K | 24 Feb, 2020, 09:15: PM
CBSE 11-science - Physics
Asked by sheikhsaadat24 | 17 Apr, 2024, 09:41: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by sy123946 | 07 Apr, 2024, 04:23: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by derhebha955 | 03 Apr, 2024, 09:03: AM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by sumedhasingh238 | 29 Mar, 2024, 05:15: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by sumedhasingh238 | 28 Mar, 2024, 11:10: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by roshnibudhrani88 | 23 Mar, 2024, 05:52: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by emad.amd | 21 Mar, 2024, 12:00: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by vinitdubey7735 | 14 Mar, 2024, 11:21: AM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by om636694 | 04 Mar, 2024, 09:10: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by rajuinwati12 | 04 Mar, 2024, 09:22: AM
ANSWERED BY EXPERT
