Gravitation

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  1. Two satellites of earth, S1 and S2 are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?








  1. View Hint View Answer Discuss in Forum

    Since orbital velocity of satellite is v = √GM / r , it does not depend upon the mass of the satellite. ​
    Therefore, both satellites will move with same speed.

    Correct Option: B

    Since orbital velocity of satellite is v = √GM / r , it does not depend upon the mass of the satellite. ​
    Therefore, both satellites will move with same speed.

  1. For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60° with the vertical, then escape velocity will be​​








  1. View Hint View Answer Discuss in Forum

    Since, escape velocity (ve - √2gRe ) is independent of angle of projection, so it will not change.

    Correct Option: A

    Since, escape velocity (ve - √2gRe ) is independent of angle of projection, so it will not change.

  1. A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is








  1. View Hint View Answer Discuss in Forum

    The velocity u should be equal to the escape velocity. That is,
    u = √2gR

    But g =
    GM
    R2

    Correct Option: A

    The velocity u should be equal to the escape velocity. That is,
    u = √2gR

    But g =
    GM
    R2

  1. A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If v1 and v2 are the linear velocities at these points respectively, then the ratio
    v1
    		 is
    v2








  1. View Hint View Answer Discuss in Forum

    Angular momentum is conserved ​
    ∴ L1 = L2 ​⇒ mr1v1 = mr2v2 ​
    ⇒ r1v1 = r2v2

    ⇒
    v1
    		 =
    r1
    v2r2

    Correct Option: B

    Angular momentum is conserved ​
    ∴ L1 = L2 ​⇒ mr1v1 = mr2v2 ​
    ⇒ r1v1 = r2v2

    ⇒
    v1
    		 =
    r1
    v2r2

  1. If ve is escape velocity and v0 is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by :​​








  1. View Hint View Answer Discuss in Forum


    ve = √2 v0

    Correct Option: D


    ve = √2 v0