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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
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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
