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A pendulum clock loses 12s a day if the ...

A pendulum clock loses 12s a day if the temperature is `40^@C` and gains 4s a day if the temperature is `20^@C`, The temperature at which the clock will show correct time, and the co-efficient of linear expansion `(alpha)` of the metal of the pendulum shaft are respectively:

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A pendulum clock loses 24 sec a day if the temperature is 60^(@)C and gains 8 sec a day if the temperature is 40^(@)C .The temperature at which the clock will show correct time.

Pendulum of a clock consists of very thin sticks of iron and an alloy. At room temperature the iron sticks 1 and 2 have length L_0 each. Length of each of the two alloy sticks 4 and 5 is 0 and the length of iron stick 3 (measured up to the centre of the iron bob) is l_0 . Thickness of connecting strips are negligible and mass of everything except the bob is negligible. The pendulum oscillates about the horizontal axis shown in the figure. It is desired that the time period of the pendulum should not change even if temperature of the room changes. Find the coefficient of linear expansion ( alpha ) of the alloy if the coefficient of linear expansion for iron is alpha_(0) .

Knowledge Check

  • A pendulam clock loses 12s a day if the temperature is 40^@C and gains 4s a day if the temperature is 20^@C , The temperature at which the clock will show correct time, and the co-efficient of linear expansion (alpha) of the metal of the pendulam shaft are respectively:

    A
    `30^@C: alpha=1.85xx10^-3//^@C`
    B
    `55^@C: alpha=1.85xx10^-2//^@C`
    C
    `25^@C: alpha=1.85xx10^-5//^@C`
    D
    `60^@C: alpha=1.85xx10^-4//^@C`

  • A pendulum clock is 5 sec. Slow at a temperature 30^(@)C and 10 sec. fast at a temperature of 15^(@)C , At what temperature does it give the correct time-

    A
    `18^(@)C`
    B
    `20^(@)C`
    C
    `25^(@)C`
    D
    None of these

  • A pendulum clock is 5 s fast at a temperature of 15^(@)C and 10 s slow at a temperature of 30^(@)C . At what temperature does it give the correct time? (take time interval = 24 hours)

    A
    `18^(@)C`
    B
    `22^(@)C`
    C
    `20^(@)C`
    D
    `25^(@)C`

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    An insulated chamber at a height h above the earth's surface and maintained at 30^(@)C has a clock fitted with an uncompensated pendulum. The maker of the clock for the chamber mistakenly design it to maintain correct time at 20^(@)C at that height. it is found that if the chamber were brought to earth's surface the clock in it would click correct time at 30^(@)C . the coefficient of linear expansion of the material of pendulum is (earth's radius is R)

    A clock with a metallic pendulum gains 5 s each day at a temperature of 15^@C and loses 10 s each day at a temperature of 30^@C . Find the coefficient of thermal expansion of the pendulum metal.

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