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Ask iit jee aieee pet cbse icse state board experts Expert Question: ans given is cos(inverse)1/4
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trisha (34)

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A small sphere is given downward vertical velocity V=5m/s and it swings (from horizontal position) in a vertical plane about the end of massless string of length 2m.Find the angle  with the vertical at which string will break,knowing that it can withstand a maximum tension equal to twice the weight of the sphere.(take g=10m/s2)
    
iitkgp_bipin (6144)

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KE when it is striked = (1/2)m(52)

Suppose its velocity is u when it makes and angle with vertical.

Gain in KE = Loss in PE
(1/2)mu2 - (1/2)m(52) = mglcos
u2 = 25 + 40 cos

Force equation at maximum tension :

Tmax - mgcos = mu2/l

2mg - mgcos = mu2/l    (since Tmax = 2mg)

2mg - mgcos = m(25+40cos)/2

4 - 2cos = 2.5 + 4cos

6cos = 1.5

cos = 1.5/6 = 1/4

Hence = cos-1(1/4)


Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur

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trisha (34)

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thank u
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