NEETPhysicsOscillations
Match List-I (Lengths of two simple pendulums) with List-II (Minimum number of oscillations of the shorter pendulum after which they are again in phase at the mean position) and select the correct option. List-I List-II (A) 144 cm and 100 cm (I) 8 (B) 64 cm and 49 cm (II) 9 (C) 81 cm and 64 cm (III) 13 (D) 169 cm and 144 cm (IV) 6
Options
- A(A) (IV), (B) (II), (C) (I), (D) (III)
- B(A) (IV), (B) (I), (C) (II), (D) (III)
- C(A) (IV), (B) (I), (C) (III), (D) (II)
- D(A) (I), (B) (IV), (C) (II), (D) (III)
Correct answer
B. (A) (IV), (B) (I), (C) (II), (D) (III)
Step-by-step solution
The time period of a simple pendulum is T l . Let the shorter pendulum complete n oscillations and the longer pendulum complete (n-1) oscillations when they are again in phase. nT_ short = (n-1)T_ long n n-1 = T_ long T_ short = l_ long l_ short For (A): 144 100 = 12 10 = 6 5 n = 6 . Matches with (IV). For (B): 64 49 = 8 7 n = 8 . Matches with (I). For (C): 81 64 = 9 8 n = 9 . Matches with (II). For (D): 169 144 = 13 12 n = 13 . Matches with (III). Therefore, the correct matching is (A) (IV), (B) (I), (C) (II), (D)