Explanation Given information: Figure-(1) Figure-(1) represents the compound pendulum with two knife edges. Write the expression for the length of the equivalent simple pendulum for knife edge A . l A = r ¯ + k ¯ 2 r ¯ ....... (I) Here, the distance between A and G is r ¯ , and the distance between B ' and G is k ¯ 2 r ¯ . Write the expression for the length of the equivalent simple pendulum for knife edge B . l B = R ¯ + k ¯ 2 R ¯ ....... (II) Here, the distance between B and G is R ¯ , and the distance between A ' and G is k ¯ 2 R ¯ . Write the expression for the time period for the knife edge A . τ A = 2 π l A g ....... (III) Here, acceleration due to gravity is g . Write the expression for the time period for the knife edge B

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 19, Problem 19.170RP

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The proof of g=4π2lτ2.

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Chapter 19, Problem 19.169RP

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If either a simple or a compound pendulum is used to determine experimentally the acceleration of gravity g, difficulties are encountered. In the case of the simple pendulum, the string is not truly weightless, while in the case of the compound pendulum, the exact location of the mass center is difficult to establish. In the case of a compound pendulum, the difficulty can be eliminated by using a reversible, or Kater, pendulum. Two knife edges A and B are placed so that they are obviously not at the same distance from the mass center G, and the distance l is measured with great precision. The position of a counterweight D is then adjusted so that the period of oscillation τ obtained is equal to that of a true simple pendulum of length l and that g 4π2 l/τ.

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The proof of g = 4 π 2 l τ 2 .

Solution Summary: The author explains how to write the expression for the length of the equivalent simple pendulum for knife edge A.

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The proof of g=4π2lτ2.

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Chapter 19 Solutions