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Question

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g=10 m/s2, then the maximum angular velocity of the stone will be

A
2 rad s1
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B
4 rad s1
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C
8 rad s1
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D
16 rad s1
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Solution

The correct option is B 4 rad s1
Maximum tension in the string will be at the lowest point of the circular path, where the tension will balance weight as well as provide the centrifugal force for circular motion.

The force equation at the bottom most point
Tmg=mω2r
mω2r=T5
For maximum angular speed, the tension must be maximum i.e. 37 N
Mass of the stone is 500 g=12 kg

ω2=32×21×r=644

ω=4 rad/s

Hence option B is the correct answer

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