Questions

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 bent in the form of a 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 0.06 m. Each spring has a natural length of 0.06$\mathrm{\pi}$ m and force constant 0.1N/m. Initially both the balls are displaced by an angle $\mathrm{\theta}=\mathrm{\pi}/6$ radian with respect to the diameter $\mathrm{PQ}$ of the circle and released from rest. The frequency of oscillation of the ball B is

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a

π Hz

b

1πHz

c

2π Hz

d

12πHz

detailed solution

Correct option is B

As here two masses are connected by two springs, this problem is equivalent to the oscillation of a reduced mass mr of a spring of effective spring constant. T=2πmrKeff.Here mr=m1m2m1+m2=m2⇒Keff.=K1+K2=2K∴n=12πKeff.mr=12π2Km×2=1πKm=1π0.10.1=1πHz

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