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
B
R1<R2
C
R2=2×R1
D
R1=R2

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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