AP EAMCET20224 Jul 2022Morning ShiftPhysicsOscillationsActual
A hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density ρ . If the mass of hydrometer is m and the radius of the hydrometer tube is r , then the time period of oscillation is
Options
- AT = 2 π m π r 2 ρ g
- BT = 2 π π r 2 ρ g m
- CT = 1 2 π m π r 2 ρ g
- DT = 1 2 π π r 2 ρ g   m
Correct answer
A. T = 2 π m π r 2 ρ g
Step-by-step solution
If the hydrometer were in equilibrium or floating, its weight will be balanced by the buoyancy force acting on it by the fluid. During its small oscillation, let us locate the hydrometer when it is a vertically downward distance x from its equilibrium position. Here, the net unbalanced force on the hydrometer is the excess buoyancy force directed upward. Thus, F b = ρ V g = ρ π r 2 x g . Now, restoring force m a = F b . So, restoring acceleration is a = - ρ π r 2 g x m . For SHM, accelerati