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Determine the period of small oscillatio...

Determine the period of small oscillations of a mathematical pendulum, that is a ball suspended by a thread `l=20 cm` in length, if it is located in a liquid whose density is `eta=3.0` times less than that of the ball. The resistance of the liquid is to be neglected.

Text Solution

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Let, V=volume of bob
`rho` =density of material of the bob
g'=effective value of acceleration due to gravity
Now , effective weight=weight of bob- upthrust of liquid
`Vrhog'=Vrhog-V(rho)/(eta)g`
`g'=(1-(1)/(eta))g "or" g'=(eta-1)/(eta)g`
Again, `T=2pisqrt((l)/(g')) " or "T=2pisqrt((l)/((eta-1)/(eta)g))`
or `T=2pisqrt((etal)/((eta-1)g))`
Substituting values, we get
`T=2xx(22)/(7)sqrt((3 xx 20xx10^(-2))/((3-1)9.8))s=(44)/(7)xx 0.175s=1.1 s`
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