Radial & Tangential Acceleration for Non Uniform Circular Motion
A stone of ma...
Question
A stone of mass 1kg tied to a light string of length 103m is whirled in a vertical circle. If the ratio of the maximum tension to minimum tension is 4 and g=10m/s2, then the speed of the stone at the highest point of the circle is
A
0m/s
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B
20m/s
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C
10m/s
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D
5m/s
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Solution
The correct option is C10m/s
Let vo & vt be the velocities at the bottom and top of the circle.
Tension will be maximum at the bottom of the circle. ⇒Tmax=mv2or+mg ------(1)
Tension will be minimum at the top of the circle. ⇒Tmin=mv2tr−mg -------(2)
TmaxTmin=4 (given) ⇒mv2or+mgmv2tr−mg=4 -----(3)
Applying conservation of energy at points A & B, taking A as a reference point KEA+PEA=PEB+KEB 12mv2o+0=mg(2r)+12mv2t v2o−v2t2=2gr -------(4)
From equation (3) mv2or+mg=4mv2tr−4mg ⇒5mg=4mv2tr−mv2or 4v2t−v2o=5gr ---------(5)
From equation (4) v2o−v2t=4gr−−−−−−−−(6)
By solving Equation (5) & (6) 3v2t=9gr v2t=3gr vt=√3gr vt=√3×10×103=10m/s