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Two identical balls A and B , each of ma...

Two identical balls A and B , each of mass 0.1 kg , are attached to two identical massless springs. The spring - mass system is constrained to move inside a rigid smooth pipe of bent in the form of circle , as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.03 m . Each spring has a natural length of `0.06pi` m and force constant `0.1 Nm^(-1)` . Initially , both the balls are displaced by an angle `theta=(pi)/6` rad , with respect to the diameter PQ of the circle , and released from rest . The frequency of oscillation of the ball B is

Text Solution

Verified by Experts

Since at P and Q both the springs are relaxed so whole energy becomes kinetic.
`:. (1)/(2) m_(1) v_(1)^(2) + (1)/(2) m_(2) v_(2)^(2) = mv^(2) = E = 4pi^(2) xx 10^(-5)`
or `(0.1) v^(2) = 4pi^(2) xx 10^(-5)`
`rArr v = 2pi xx 10^(-2) m//s`
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