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CIRCULAR MOTION (i) If velocity becomes zero at height h 1 O = u 2 – 2gh, or h 1 = 2 u 2g ........ (v) (ii) If tension becomes zero at height h 2 O = m r [u 2 + gr – 3gh 2 ] or u 2 + gr – 3gh 2 = 0 or h 2 = 2 u gr 3g + .........(vi) (iii) Case of oscillation It v = 0, T 0 then h 1 < h 2 2 2 u u gr 2g 3g + < 3u 2 < 2u 2 + 2gr u 2 < 2gr u < 2gr (iv) Case of leaving the circle If v 0, T = 0 then h 1 > h 2 2 2 u u gr 2g 3g > 3u 2 > 2u 2 + 2gr u 2 > 2gr u > 2gr 5gr u 2gr > > (v) Case of complete the circle u 5gr T 0 v 0 v=0, T0 v 2gr < < Case of oscillation = Case of oscillation semi-circular path T=0 v=0 T=0 v=0 u 2gr < u A α α v 0 T = 0 v Parabolic path Case of leaving the circle 5gr u 2gr > > > > u > 5gr Case of complete the circle or looping the loop

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Transcript of 14

  • CIRCULAR MOTION

    (i) If velocity becomes zero at height h1O = u2 2gh,

    or h1 = 2u

    2g ........ (v)

    (ii) If tension becomes zero at height h2

    O = mr

    [u2 + gr 3gh2]

    or u2 + gr 3gh2 = 0

    or h2 = 2u gr3g+

    .........(vi)

    (iii) Case of oscillationIt v = 0, T 0then h1 < h2

    2 2u u gr2g 3g

    + h22 2u u gr

    2g 3g+

    >

    3u2 > 2u2 + 2gr

    u2 > 2gr

    u > 2gr

    5gr u 2gr> >

    (v) Case of complete the circle

    u 5gr T 0

    v 0

    v=0,T 0

    v 2gr >> >

    u > 5gr

    Case of completethe circle or

    looping the loop