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Question

Two identical tall jars are filled with water to the brim. The first jar has a small hole on the side wall at a depth $$h/3$$ and the second jar has a small hole on the side wall at a depth of $$2h/3$$, where h is the height of the jar. The water issuing out from the first jar falls at a distance $$R_{1}$$ from the base and the water issuing out from the second jar falls at a distance $$R_{2}$$ from the base. The correct relation between $$R_{1}  \ and \  R_{2}$$ is


A
R1>R2
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B
R1<R2
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C
R2=2×R1
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D
R1=R2
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Solution

The correct option is D $$R_{1} = R_{2}$$
At  any  height  h  from  surface, velocity  $$V = \sqrt{2gh}$$
Time  of  flight $$ t = \sqrt{\dfrac{2(H-h)}{g}}$$
where $$H$$ is the total height of jar. 
$$ \therefore$$  Range  $$R = V\times t$$
$$R = 2\sqrt{h(H-h)}$$
Given, $$   h_{1} = \dfrac{h}{3} \  and  \ H=h$$
$$ \Rightarrow $$ $$R_1 = 2\sqrt{\dfrac{h}{3}(h-\dfrac{h}{3})}$$ $$  = \dfrac{2\sqrt{2}h}{{3}}$$
For $$  \  h_{2} = \dfrac{2h}{3}\  and \  H=h$$
$$ \Rightarrow $$ $$R_2 = 2\sqrt{\dfrac{2h}{3}(h-\dfrac{2h}{3})}$$ $$  = \dfrac{2\sqrt{2}h}{{3}}$$
$$\therefore  R_{1} = R_{2}$$

Physics

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