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Question

Particles each of mass m are tied by means of strings of equal length as shown in figure. If the system is rotated with constant angular velocity ω in horizontal plane, find the tension in the string.
[Given ris the radius of the circle]


A
mrω22
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B
mrω25
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C
mrω22
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D
mrω222
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Solution

The correct option is A mrω22
Free body diagram of single mass (D) ,


From FBD, a single mass will have two tensions at an angle of 90o as it forms a square, so by the law of vector addition the net resultant tension(T) will be

T=T2+T2+2T2cos900= T2 and the resultant tension Twill provide the necessary centripetal force.
Hence T=mrω2
T2=mrω2T=mrω22

Hence option A is the correct answer.

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