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Q.

On the surface of earth acceleration due to gravity is g and gravitational potential is V. Match the Column I with Column II and mark the correct option from the codes given below.Column I(A) At height h = R, value of g(B) At depth h = R2, value of g(C) At height h = R, value of V(D) At depth h = R2, value of V Column II(p) decreases by a factor 14(q) decrease by a factor 12(r) decrease by a factor  118(s) increases by a factor 2(t)  None

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a

A B C Dp  t  s  r

b

A B C Dq t q r

c

A B C Dq r p s

d

A B C Dp q q r

answer is D.

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Detailed Solution

As  g=GMR2,V=-GMRAt height   h=R,g=g1+hR2=g4⇒V'=-GM2Ri.e. g decrease by a factor 1/4 and V also decreases by a factor of 1/2.At depth  h=R2g'=g1-hR=g1-12=g2V'=-GMR315R2-0.5r2=-GMR315R2-18R2=-118GMRi.e. g decrease by a factor 12 and V' also decreases by a factor 118.
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