IIT JEE , AIEEE Forum - Physics , Mechanics

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What will b the value of g if bob of simple pendulum is made to oscillate in some fluid of density d? What will be the time period of a simple pendulum if length of the pendulum is comparable to radius of the earth?

Expian clearly

edison

Problem) What will b the value of g if bob of simple pendulum is made to oscillate in some fluid of density d?

Solution) If density of bob material is = d₁

Also if volume of the bob = V

Density of fluid in which simple pendulum is oscillating = d₂

Then the buoyancy force due to fluid on the bob = F_b = V d₂g (against gravity)

So, Resultant Force on the bob is given by = Gravitaional force - Buoyancy force

Or Resultant force on the bob = V d₁ g - V d₂g

If effective acceleration due to gravity = g' then above equation can be written as

V d₁g' = V d₁ g - V d₂g

or, g' = (d₁ - d₂) g / d₁

edison

So Time period of the simple pendulum in the fluid is given by

T = 2 pi ( l / g' )^1/2

where g' is given by above mentioned expression i.e.

g' = (d1 g - d2g) / d1

edison

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