Two rocks are tied to massless strings and whirled in nearly horizontal circles so that the...

Two rocks are tied to massless strings and whirled in nearly horizontal circles so that the time to travel around the circle once is the same for both. Once string is three times as long as the other. The tension in the longer string is four times the tension in the shorter one. What is the mass m1 of the rock at the end of the shorter string compared to the mass m2 of the rock at the end of the longer one?

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Expert Solution

Let m1, 1,F1 and m2, 2, F2 be the mass length and tension in the short and long string respectively. Given the time to travel around the circle is same for both. That means the time period (T) is same for both. The tme period and angular velocity () is related as,

Since T is same for both, the angular velocities of both wil be same. That is,

When a body is executing horizontal circular motion, the tension (F) in the string provides the necessary centripetal force for the circular motion. So

where r is the radius of the circle. Here r = l. So,

For the short string,

For the long string,

Dividing both the equations,

But given 2 = 3 1 and F2 = 4F1. Therefore,

genius_generous answered 1 year ago

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