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Standard XII

Physics

Applications of Horizontal and Vertical Components

A ball of rad...

Question

A ball of radius r and density r 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 h, the value of h is given by

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Solution

The correct option is C
Velocity of ball when it strikes the water surface v = $\sqrt{2 g h}$ ..........(i)
Terminal velocity of ball inside the waterv= $\frac{2}{9} r^{2} g \frac{(ρ - 1)}{η}$ ..........(ii)
Equating (i) and (ii) we get $\sqrt{2 g h} = \frac{2}{9} \frac{r^{2} g}{η} (ρ - 1) \Rightarrow h = \frac{2}{81} r^{4} {(\frac{ρ - 1}{η})}^{2} g$

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A ball of radius r and density r 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 h, the value of h is given by

The correct option is C Velocity of ball when it strikes the water surface v =√2gh ..........(i) Terminal velocity of ball inside the waterv=29r2 g(ρ−1)η ..........(ii) Equating (i) and (ii) we get √2gh=29r2gη(ρ−1)⇒h=281r4(ρ−1η)2g