A satellite of mass m revolves around the earth of radius R at a

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 Multiple Choice QuestionsMultiple Choice Questions

11.

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

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12.

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.

222 Views

13.

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

654 Views

14.

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

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15.

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

247 Views

16.

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between
(you may take G = 6 . 67× 10-11 Nm2/ kg2)

  • 13.34 x 10-10 J

  • 3.33 x 10-10 J

  • 6.67 x10-9 J

  • 6.67 x10-9 J

213 Views

17.

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

  • moment of inertia

  • angular momentum

  • angular velocity

  • angular velocity

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18.

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

  • fraction numerator gR over denominator straight R minus straight x end fraction
  • gx

  • fraction numerator gR squared over denominator straight R space plus straight x end fraction
  • fraction numerator gR squared over denominator straight R space plus straight x end fraction


D.

fraction numerator gR squared over denominator straight R space plus straight x end fraction

The gravitational force exerted on satellite at a height x is

straight F subscript straight G space equals space fraction numerator GM subscript straight e straight m over denominator left parenthesis straight R plus straight x right parenthesis squared end fraction
where Me = mass of earth Since, gravitational force provides the necessary centripetal force, so,

fraction numerator GM subscript straight e straight m over denominator left parenthesis straight R plus straight x right parenthesis squared end fraction space equals space fraction numerator mv subscript 0 superscript 2 over denominator left parenthesis straight R plus straight x right parenthesis end fraction
rightwards double arrow space fraction numerator GM subscript straight e straight m over denominator left parenthesis straight R plus straight x right parenthesis end fraction space equals space mv subscript 0 superscript 2
rightwards double arrow space fraction numerator begin display style gR squared straight m end style over denominator left parenthesis straight R plus straight x right parenthesis end fraction space equals space mv subscript 0 superscript 2
rightwards double arrow space fraction numerator begin display style gR squared straight m end style over denominator left parenthesis straight R plus straight x right parenthesis end fraction space equals space mv subscript 0 superscript 2 space
open parentheses because space straight g space equals space fraction numerator begin display style GM subscript straight e end style over denominator straight R end fraction close parentheses
straight v subscript straight o space equals space square root of open square brackets fraction numerator gR squared over denominator left parenthesis straight R plus straight x right parenthesis end fraction close square brackets end root
space equals space open square brackets fraction numerator gR squared over denominator left parenthesis straight R plus straight x right parenthesis end fraction close square brackets to the power of 1 divided by 2 end exponent

619 Views

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19.

The time period of an earth satellite in circular orbit is independent of

  • the mass of the satellite

  • radius of its orbit

  • both the mass and radius of the orbit

  • both the mass and radius of the orbit

552 Views

20.

If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

  • 2 mgR

  • mgR/2

  • mgR/4

  • mgR/4

298 Views

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