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AP EAMCET201823 Apr 2018Evening ShiftPhysicsOscillationsActual

One end of a long metallic wire of length L , area of cross-section A and Young's modulus Y is tied to the ceiling. The other end is tied to a massless spring of force constant k and a mass m is hung from the free end of the spring. If m is slightly pulled down and released, then its time period of oscillation is

Options

  1. A2 m k
  2. B2 m Y A k L
  3. C2 m(k A+Y L) k Y A
  4. D2 m(k L+Y A) k Y A

Correct answer

D. 2 m(k L+Y A) k Y A

Step-by-step solution

For oscillating mass at end of a rod. Restoring force = Y A L x So, k₁= spring constant for a rod is Y A L . If a rod and spring are connected, then it is a series combination. So, (k_ eq ) aligned system & = k₁ k₂ k₁+k₂ & = k Y A / L k+ Y A L = k Y A k L+Y A aligned So, T=2 m k_ e q T=2 m(k L+Y A) k Y A

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