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A liquid of mss m is set into oscillatio...

A liquid of mss m is set into oscillations in a U-tube of cross section A. Its time period recorded is T, where `T=2pisqrt(l//2g)` , here l is the length of liquid column. If the liquid of same mass is set into oscillations in U-tube of cross-section A/16 then determine time period of oscillation.

Text Solution

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As mass is constant
`therefore` Volumn x density =constant (`because` Density=`("Mass")/("Volumn"))`
`implies V_(1)d=V_(2)d`
where , `V_(1)` and `V_(2)` are the volumn of liquid in U-tube in two cases respectively
`(Al)d=|(A)/(16)l'| dimplies l'=16l`
`because T=2pisqrt((1)/(2g))`
`therefore (T')/(T)=sqrt((l')/(l))=sqrt((16l)/(l))=4 impliesT'=4T`
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