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Question

The sphere at 'A' is given a downward velocity v0 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 four times the weight of the sphere. Find the value of v0.(g=10m/s2)
1190916_df6cf81a96774e67ac12dbc2ba366eb7.jpg

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Solution

Solution
Wgravity=mg(l2)
KE=wgravity
[work energy theorem]
mv22mvo22=mgl2 __ (1)
Also,
Tmg2=mv2l __ (ii)
From (i) and (ii),
12(Tmg2)lmv022=mgl2
12(4mgmg2)lmvo22=mgl2
74mglmvo22=mgl2
2m[7mgl4mgl2]=vo2
Vo=52gl

1156211_1190916_ans_a24dcbc91b724049be85e0f7a2af6b2a.jpg

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