If gE and gm are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the moon/ electronic charge on the earth) to be

  • 1

  • 0

  • gE/gM

  • gE/gM


A.

1

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Average density of the earth

  • does not depend on g

  • is a complex function of g

  • is directly proportional to g

  • is directly proportional to g


C.

is directly proportional to g

straight g space equals space fraction numerator straight G 4 straight pi over denominator 3 end fraction straight rho subscript av straight R
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The change in the value of g at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of earth, then which one of the following is correct?

  • d =h/2

  • d=3h/2

  • d =2h

  • d =2h


C.

d =2h

fraction numerator GM over denominator left parenthesis straight R plus straight h right parenthesis squared end fraction space equals space GM over straight R cubed left parenthesis straight R minus straight d right parenthesis
rightwards double arrow space straight d space equals 2 straight h
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A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms−1, the escape velocity from the

  • 1.1 kms−1

  • 11 kms−1

  • 110 kms−1

  • 110 kms−1


C.

110 kms−1

straight V subscript esc space equals space square root of fraction numerator 2 GM over denominator straight R end fraction end root space equals space square root of fraction numerator 2 straight G space straight x space 10 space straight M over denominator straight R divided by 10 end fraction end root space
space equals space 10 space straight x space 11 space equals space 110 space km divided by straight s
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This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement – I:
For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is 4π GM.
and
Statement – II
If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as 1/r2, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

  • Statement – 1is false, Statement – 2 is true.

  • Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

  • Statement – 1 is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

  • Statement – 1 is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.


B.

Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

g = GM/r2

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