HSC Science (General) 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Derive an Expression for Acceleration Due to Gravity at Depth ‘D’ Below the Earth’S Surface. - HSC Science (General) 12th Board Exam - Physics

Login
Create free account


      Forgot password?

Question

Derive an expression for acceleration due to gravity at depth ‘d’ below the earth’s surface.

Solution

 
 

Let M be mass of the earth, R be the radius of the earth

gd be gravitational acceleration at depth 'd ' from the earth surface

g be gravitational acceleration on the earth surfaces.

ρ be the density of the earth.

‘P’ be the point inside the eaarth at depth 'd ' from earth surfaces.

∴ CS-CP=d, ∴ CP=R-d .............(1)   (since CS=R)

`g=(GM)/R^2`,

`therefore g=(G4/3piR^3rho)/R^2`

`therefore g=(4GpiRrho)/3`  ....(2)

gd = acceleration due to gravity at depth 'd '

`g_d=(Gxx"Mass of the sphere with radius CP")/(CP^2)`

`thereforeg_d=(G4/3piCP^3rho)/(CP^2)`

`thereforeg_d=(4GpiCPrho)/3` .... (3)

Dividing eq. (3) by eq. (2)

`g_d/g=(CP)/R=(R-d)/R`

`therefore g_d=g(1-d/R)`

c

 

 
  Is there an error in this question or solution?

APPEARS IN

 2013-2014 (March) (with solutions)
Question 2.1 | 3.00 marks
Solution Derive an Expression for Acceleration Due to Gravity at Depth ‘D’ Below the Earth’S Surface. Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth.
S
View in app×