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Question

A clock while keeps correct time at 30C has a pendulum rod made of brass. The number of seconds it gains (or) looses per second when the temperature falls to 10C is
[α of brass = 18×106/C]

A
18×106sec
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B
18×105sec
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C
0)0018 sec
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D
0)018 sec
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Solution

The correct option is A 18×105sec

We know, α=dl/(dt×l)

or, dl=α×dt×l -----(1)

Now T=2πl/g --- (2)

or, T+dT=2π(l+dl)/g

or, T(1+dT/T)=2πl/g1+dl/l ----- (3)

Using (2)

1+dT/T=(l+dl/l)1/2

1+dT/T=1+(1/2)dl/l

dT/T=(1/2)(dl/l)

dT=(1/2)(dl/l)T

Using (1)

dT=(1/2)[(αdtl)/l]XT

=(1/2)×18×106××1

=18×105


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