A ball of radius r and density ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is η, the value of h is given by

Question

A ball of radius r and density ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is η, the value of h is given by, 2 9 r 2 ( 1 - ρ η ) g, 2 81 r 2 ( ρ - 1 η ) g, 2 8 1 r 4 ( ρ - 1 η ) 2 g, 2 9 r 4 ( ρ - 1 η ) 2 g

MARKS App · Accepted Answer

Velocity of ball when the water surface v = 2 gh ............ i Terminal velocity of ball inside the water v = 2 9 r 2 g ρ - 1 η ............ i i Equating (i) and (ii)we get 2 gh = 2 9 r 2 g η ρ - 1 ⇒ h = 2 8 1 r 4 ( ρ - 1 η ) 2 g

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