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A simple pendulum has a time period T in...

A simple pendulum has a time period T in vacuum. Its time period when it is completely immersed in a liquid of density one-eight of the density of material of the bob is

A

`sqrt((7)/(9)) T`

B

`sqrt((5)/(8))` T

C

`sqrt((3)/(8))T`

D

`sqrt((8)/(7))T`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) In vacuum, `T=2pisqrt((l)/(g))`
Let V be the volume and T be the density of the mass of the bob. Net downward force acting on the bob in the side the liquid =Weight-upthrust=`Vrhog-V.(T)/(8)g=(7)/(8)Vrhog`

i.e., effective value of g is `(7)/(8)g`
So, time period of the bob inside the liquid
`T_(1)=2pisqet((1)/((7//8)g))=2pisqrt((l)/(g))xx sqrt((8)/(7))=sqrt((8)/(7))T`.
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