8.2 Choose the correct alternative:

(a) Acceleration due to gravity increases/decreases with increasing altitude

 

(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density)

 

(c) Acceleration due to gravity is independent of mass of the earth/mass of the body

 

(d) The formula –G Mm(1/r2 – 1/r1) is more/less accurate than the formula mg(r2 r1) for the difference of potential energy between two points r2 and r1 distance away from the centre of the earth

0 6 Views | Posted 4 months ago
Asked by Shiksha User

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  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    (a) Decreases - Acceleration due to gravity at depth h is given by gh = (1 – 2hRe )g, where Re=Radiusoftheearth, g = acceleration due to gravity on the surface of the Earth. From this equation, it is clear that acceleration due to gravity decreases with increase in height

     

    (b) Decreases – Acceleration due to gravity at depth d is given by gd = (1- dRe )g. So the acceleration due to gravity decreases with increase in depth.

     

    (c) Mass of the body – Acceleration due to gravity of body mass m is given by the relation g = GMR2 , where G = Universal gravitation constant, M = mass of the Earth and R = radiu

    ...more

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Kindly go through the solution

 

A
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  G M m ( R + x ) 2 = G M m ( R x ) R 3

->R3 = (R + x)2 (R – x)

->R3 = (R2– x2) (R + x)

->x2 + Rx – R2 = 0


x = R ± R + 4 R 2 2

x = ( 5 R 1 ) 2 R

           

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Stress = F A = T A = W A

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Vishal Baghel

( v e ) A = ( v e ) B M 1 R 1 = M 2 R 2

R is not correct.

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F 1 = G M m 9 R 2

F 2 = G M m 9 R 2 G M 8 m ( 5 R 2 ) 2 = G M m R 2 ( 1 9 1 5 0 )

F 1 F 2 = 1 1 9 5 0 = 5 0 4 1

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