Figure below shows a shampoo bottle in a perfect cylindrical shape In a simple experiment, the stability of the bottle filled with different amount of shampoo volume is observed. The bottle is tilted from one side and then released. Let the angle θ depicts the critical angular displacement resulting in the bottle losing its stability and tipping over. Choose the graph correctly depicting the fraction f of shampoo fil

Step-by-step solution

Mass of bottle = m 0 Length of bottle = L base Area = A = π r 2 density of shampoo = ρ mass of shampoo = ρ f A L Center of mass of system y = m 0 L 2 + ρ f A L f L 2 m 0 + ρ f A L for critical angular displacement, m g will pass through tilted side. From the diagram tan θ = r y tan θ = r m 0 + ρ A L f L 2 m 0 + ρ A L f 2 at f = 0 & f = 1 , tipping angle θ will be same. for very small values of f , we can neglect f 2 terms ⇒ tan θ = r L 2 m 0 + ρ A L f m 0 θ = tan - 1 r L 2 m 0 + ρ A L f m 0 So if f increases θ will