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A bob of simple pendulum is suspended by...

A bob of simple pendulum is suspended by a metallic wire. If `alpha` is the coefficient of linear expansion and `d theta` is t he change in temperature then prove that percentage change in time period is `50 alpha d theta`.

Text Solution

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With change in temperature `d theta` , the effective length of wire becomes `l'=l(1+alpha d theta)`
`T'=2pisqrt((l')/(g)) "and " T=2pisqrt((l)/(g))`
Hence, `(T')/(T)=sqrt((l')/(l))=(1+alphad theta)^(1//2)=1+(1)/(2)alphad theta`
Percentage increase in time period
`((T'-T)/(T))xx100((T')/(T)-1)xx 100`
`(1+(alphad theta)/(2)-1) xx 100 =50 alpha d theta`
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