KVPY SX SB Exam 2016 Question Paper

Question : 91 of 120

Marks: +1, -0

PHYSICS

A light balloon filled with helium of density

\ρ_\He

is tied to a long light string of length l and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released then .

The ballon undergoes simple harmonic motion with period $2π√{(\ρ_\air/{\ρ_\air-\ρ_\He})l/g}$
The ballon undergoes simple harmonic motion with period $2π√{({\ρ_\air-\ρ_\He}/\ρ_\air)l/g}$
The ballon undergoes simple harmonic motion with period $2π√{(\ρ_\He/{\ρ_\air-\ρ_\He})l/g}$
The ballon undergoes conical oscillations with period $2π√{({\ρ_\air+\ρ_\He}/{\ρ_\air-\ρ_\He})l/g}$

Validate

Solution:

τ_0 = V (\ρ_\Air - \ρ_\He) g l \sin θ

For small angular displacement (θ)

τ_0 = V (\ρ_\Air - \ρ_\He) g lθ

Iα = V [\ρ_\Air - \ρ_\He] g lθ

\ρ_\He V l^2 α = V [\ρ_\Air - \ρ_\He] lθ g

α=[{\ρ_\Air - \ρ_\He}/ \ρ_\He]g/lθ

ω=√{[{\ρ_\Air - \ρ_\He}/ \ρ_\He]g/l}

=2π√{(\ρ_\He/{\ρ_\air-\ρ_\He})l/g}

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