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A clock with a metallic pendulum gains 5...

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.

A

`2.3 xx 10^(-5)//.^(@)C`

B

`4.2 xx 10^(-5)//.^(@)C`

C

`5.6 xx 10^(-5)//.^(@)C`

D

`8.4 xx 10^(-5)//.^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
B
Tension 'T' at a distance x from axis.
`T=(m)/(l)(l-x)[omega^(2)(x+(l-x)/(2))]`
Stress = y strain
`(T)/(A)=Y(dDeltal)/(dx)=intdDeltal=int(T)/(AY)dx`
`Deltal=(1)/(AY)int(m)/(2l)(l^(2)-x^(2))omega^(2)dx`
`Deltal=(m)/(2AYl)omega^(2)underset(0)overset(l)int(l^(2)-x^(2))dx`
`Deltal=(momega^(2))/(2AYl)(l^(3)-(l^(3))/(3))`
`Deltal=(momega^(2))/(2AYl)(2l^(3))/(3)=(momega^(2)l^(2))/(3AY)`
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Knowledge Check

  • A clock with a metallic pendulum gains 6 seconds each day when the temperature is 20^(@)C and loses 6 second when the temperature is 40^(@)C . Find the coefficient of linear expansions of the metal.

    A
    `1.4xx10^(-5) "^(@)C^(-1)`
    B
    `1.4xx10^(-6) "^(@)C^(-1)`
    C
    `1.4xx10^(-4) "^(@)C^(-1)`
    D
    `1.4xx10^(-6) "^(@)C^(-1)`

  • A clock with a metallic pendulum gains 5 seconds each day at 22^@C and loses 10 seconds each day at 45^@C . Then,

    A
    clock keeps correct time at t `79/3 ""^@C`
    B
    clock keeps correct time at t=`89/3 ""^@C`
    C
    coefficient of linear expansion of metallic pendulum is `2.1 xx 10^(-5) ""^@C^(-1)`
    D
    coefficient of linear expansion of metallic pendulum is `1.5 xx 10^(-5) C^(-1)`

  • 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

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