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The sphere at P is given a downward velocity vo and swings in a vertical plane at the end of a rope of l = 1 m attached to a support at O.
The rope breaks at angle 30° from horizontal, knowing that it can withstand a maximum tension equal to three times the weight of the sphere. The value of vo will be: ( g =π2 m/s2)
applying energy conservaion
1/2 mvo2 + mglsin@ = 1/2 mv2 ................1
when bob is at @ = 30 then
T - mgsin30 = mv2/l
T =3mg so
mv2 = 5mgl/2 ..............2
from 1 & 2
we get
1/2 mvo2 = 5mgl/4 - mgl/2 = 3mgl/4
vo = (3gl/2)1/2 = 3.8m/s
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