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NEETPhysicsThermal Properties of Matter

A temperature-compensated pendulum is designed such that its effective length is the difference between the length of a central steel rod and the effective length of parallel brass rods. To ensure the time period remains constant at all temperatures, this effective length must not change with temperature. If the required constant effective length is 30 cm , what should be the actual length of the central steel rod? (

Options

  1. A90 cm
  2. B60 cm
  3. C45 cm
  4. D18 cm

Correct answer

A. 90 cm

Step-by-step solution

For the effective length ( L_s - L_b ) to remain constant at all temperatures, the change in length of the steel rod must equal the change in length of the brass rods. L_s = L_b L_s _s T = L_b _b T L_s _s = L_b _b L_b = L_s ( _s _b ) = L_s ( 1.2 10⁻⁵ 1.8 10⁻⁵ ) = 2 3 L_s Given the effective length is 30 cm : L_s - L_b = 30 cm L_s - 2 3 L_s = 30 cm L_s 3 = 30 cm L_s = 90 cm Answer: 90 cm

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