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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 π m and spring constant 0 . 1 N m - 1 , I

Options

  1. A1 2 π Hz
  2. B1 3 π Hz
  3. C1 π Hz
  4. D1 4 π Hz

Correct answer

C. 1 π Hz

Step-by-step solution

Given, Mass of each block A and B, m = 0.1 kg Radius of circle, R = 0 . 06 m The natural length of spring l 0 = 0.06 π = π R (Half circle) and spring constant, k = 0 . 1 N m - 1 In the stretched position elongation in each spring x = R θ Let us draw FBD of A Spring in lower side is stretched by 2x and on upper side compressed by 2x. Therefore, a force 2kx on each block would be exerted by each spring. Hence, a restoring force, F = 4kx will act on A in the direction shown in figure. Restoring torque of this force ab

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