KVPY2016PhysicsOscillations
A light balloon filled with helium of density _ He is tied to a long light string of length and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released then.
Options
- AThe ballon undergoes simple harmonic motion with period 2 ( _ air _ air - _ He ) g
- BThe ballon undergoes simple harmonic motion with period 2 ( _ air - _ He _ air ) g
- CThe ballon undergoes simple harmonic motion with period 2 ( _ He _ air - _ He ) g
- DThe ballon undergoes conical oscillations with period 2 ( _ air + _ He _ air - _ He ) g
Correct answer
C. The ballon undergoes simple harmonic motion with period 2 ( _ He _ air - _ He ) g
Step-by-step solution
₀= V ( _ Air - _ He ) g For small angular displacement ( ) array l ₀= V ( _ Air - _ He ) g I = V [ _ Air - _ He ] g _ He V ² = V [ _ Air - _ He ] g = [ _ Air - _ He _ He ] g = ( _ Air - _ He _ He ) g =2 g _ He ( _ Air - _ He ) array