Gravitation

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  1. A ball is dropped from a satellite revolving around the earth at a height of 120 km. The ball will








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    The orbital speed of satellite is independent of mass of satellite, so the ball will behave as a satellite and will continue to move with the same speed in the original orbit.

    Correct Option: B

    The orbital speed of satellite is independent of mass of satellite, so the ball will behave as a satellite and will continue to move with the same speed in the original orbit.

  1. The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth’s mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become








  1. View Hint View Answer Discuss in Forum

    Escape velcocity

    Given Me' = 2 Me and Re' =
    Re
    2


    = √4 = 2
    ve' = 2 ve = × 11.2 = 22.4 km/s

    Correct Option: B

    Escape velcocity

    Given Me' = 2 Me and Re' =
    Re
    2


    = √4 = 2
    ve' = 2 ve = × 11.2 = 22.4 km/s

  1. The escape velocity of a sphere of mass m is given by (G = Universal gravitational constant; M = Mass of the earth and Re = Radius of the earth)​​​








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    Escape velocity is the minimum velocity with which a body is projected to escape from earth's gravitational field

    1
    		mve2 =
    GMm
    		mve2 ⇒ ve = √2GM / Re
    2Re

    Correct Option: B

    Escape velocity is the minimum velocity with which a body is projected to escape from earth's gravitational field

    1
    		mve2 =
    GMm
    		mve2 ⇒ ve = √2GM / Re
    2Re

  1. The escape velocity on the surface of earth is 11.2 km/s. What would be the escape velocity on the surface of another planet of the same mass but 1/4 times the radius of the earth? ​​








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    vearth = √2GMe / Re

    ∴ vplanet = 2 × vearth = 2 × 11.2 = 22.4 km/s

    Correct Option: A

    vearth = √2GMe / Re

    ∴ vplanet = 2 × vearth = 2 × 11.2 = 22.4 km/s

  1. ​For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is​​








  1. View Hint View Answer Discuss in Forum

    K.E. of satellite moving in an orbit around the earth  is

    K =
    1
    		mv2 =
    1
    		m √GM / r 2 =
    GMm
    222r

    P.E. of satellite and earth system is
    U =
    GMm
    		⇒
    K
    		 =
    GMm
    2r =
    1
    rU
    GMm
    		2
    r

    Correct Option: A

    K.E. of satellite moving in an orbit around the earth  is

    K =
    1
    		mv2 =
    1
    		m √GM / r 2 =
    GMm
    222r

    P.E. of satellite and earth system is
    U =
    GMm
    		⇒
    K
    		 =
    GMm
    2r =
    1
    rU
    GMm
    		2
    r