The figure shows 4 different oscillating systems. The object in system C and sys

Question

The figure shows 4 different oscillating systems. The object in system C and system Dis a uniformly dense solid cylinder which rolls without slipping around an axis through its center as it oscillates. All springs are identical and the mass of each oscillating object is the same. Rank the period of the oscillations of the systems. (A) T_B > T_A > T_D > T_C (B) T_C > T_A > T_B > T_D (C) T_B > T_D > T_C > T_A (D) T_C > T_A > T_D > T_B (E) T_B > T_D > TA > T_C

Explanation / Answer

For A and b

T = 2× 3.14 (m/k)^1/2

And for C and D

T = 2 ×3.14×{ m ×(1+d^2 / R^2)/k}^1/2

Where k is spring construction

d is radius of gyration

R is radius of cylinders

m is mass

Accordingly option D suits the best.

I hope this was helpful. Thanks

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