A cubical box of wine has a small spout locat | vedclass

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(D) According to Torricelli's Theorem,the velocity of efflux,i.e.,the velocity with which the liquid flows out of a hole,is equal to $\sqrt{2gh}$,wher

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$\frac{v_0}{\sqrt[4]{2}}$

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(D) According to Torricelli's Theorem,the velocity of efflux,i.e.,the velocity with which the liquid flows out of a hole,is equal to $\sqrt{2gh}$,where $h$ is the depth of the hole below the liquid surface.Let the side of the cube be $a$. When the box is full,the depth of the spout below the liquid surface is $h = a$. Therefore,the initial speed is:$v_0 = \sqrt{2ga}$When the cubical box is half empty and tilted at $45^{\circ}$ such that the spout is at the lowest point,the liquid surface forms a plane passing through the diagonal of the cube. The height of the liquid surface above the spout is equal to the distance from the bottom corner to the diagonal plane,which is half the length of the face diagonal of the cube:$h' = \frac{\sqrt{2}a}{2} = \frac{a}{\sqrt{2}}$Now,the speed of the wine from the spout is:$v' = \sqrt{2gh'} = \sqrt{2g \left( \frac{a}{\sqrt{2}} \right)} = \sqrt{\frac{2ga}{\sqrt{2}}} = \frac{\sqrt{2ga}}{\sqrt[4]{2}} = \frac{v_0}{\sqrt[4]{2}}$

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