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A simple pendulum has a time period T₀ when oscillating in stationary air. Match the physical environments given in List-I with the corresponding new time periods given in List-II. List-I List-II (A) Immersed in a non-viscous liquid of density half that of the bob (I) T₀ 2 (B) Immersed in a non-viscous liquid of density 8 9 times that of the bob (II) 2 T₀ (C) In air, inside an elevator accelerating upwards with accel

Options

  1. A(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
  2. B(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
  3. C(A)-(II), (B)-(III), (C)-(I), (D)-(IV)
  4. D(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Correct answer

C. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)

Step-by-step solution

The time period of a simple pendulum is given by T = 2 l g_ eff . (A) When immersed in a liquid of density _L = _S 2 , the effective acceleration due to gravity is: g_ eff = g (1 - _L _S ) = g (1 - 1 2 ) = g 2 T_A = 2 l g/2 = 2 (2 l g ) = 2 T₀ . (B) When immersed in a liquid of density _L = 8 _S 9 : g_ eff = g (1 - 8 9 ) = g 9 T_B = 2 l g/9 = 3 (2 l g ) = 3T₀ . (C) In an elevator accelerating upwards with a = g , the pseudo force acts downwards: g_ eff = g + a = g + g = 2g T_C = 2 l 2g = 1 2 (2 l g ) = T₀ 2 . (D) I

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