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Q.

On the surface of earth, the gravitational field is Eg and gravitational potential is V(R = radius of earth).

 Column-I Column-II
i.At a height h = R, value of Egp.decreases by a factor 14
ii.At a depth d = R2, value of Egq.decreases by a factor 12
iii.At a height h = R, value of Vr.increases by a factor 118
iv.At a depth d = R2, value of Vs. increases by a factor 2
  t.decreases by a factor 118

Match the given columns and select the correct option from the codes given below.

Codes

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a

i-p, ii-q, iii-s, iv-t

b

i-s, ii-r, iii-t, iv -p

c

i-r, ii-s, iii-p, iv-q

d

i-p, ii-q, iii-r, iv-s

answer is C.

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Detailed Solution

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Eh = GM(R+h)2= GM4R2= E4

    Vh = -GM2R = -V2

       Ed = E(1-dR)= E2

    Vd = -GM2R3(3R3-r2)

          = -GM2R3(3R2-R24) = -11GM8R

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