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Paragraph: Four elastic cords each of force constant K and almost zero relaxed lengths are connected at their one end to a particle P of mass m and the other ends are connected to diametrically opposite points of two perpendicular diameters AC, BD. Mass of the ring is uniformly distributed and is 2 m . In equilibrium the system stays at rest with the particle at the center of the ring O ^2 . O ^ coincides at this ins

Options

  1. A2 r ₀ 3 t
  2. B- r₀ 3 t
  3. Czero
  4. Dr₀ 3 (1- t)

Correct answer

D. r₀ 3 (1- t)

Step-by-step solution

For keq So Net restoring force along Displace went aligned & =2 k r₀ 37^ 33^ +e^k r₀ 53^ 3^ & =2 k r₀ ( ( 4 3 )^2+ ( 3 5 )^2 ) & =2 k r₀ aligned Reduce mass of system = 2 m m 3 m = 2^m 3 so Time period =2 m 3 k Amplitude of motion of center of ring = r₀ 3 at t=0 centre of ring is at exteome position so x_r= 3 (1- t)

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