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A paraboloid-shaped container (cross-section given by x² = 2y) is placed with its vertex at the origin and filled with liquid to a height of 2 m. A small opening of area 10 cm² is made at the origin (vertex). Take pi = sqrt(10) and g = 10 m/s². Which of the following are correct? (A) Speed of efflux when liquid height is 0.8 m is 2 m/s (B) Speed of efflux when liquid height is 0.2 m is 2 m/s (C) Time to empty the container is 20/27 hr (D) Time to empty the container is 27/20 hr

1. speed of efflux when height of liquid is 0.8 m is 2 m/s
2. speed of efflux when height of liquid is 0.2 m is 2 m/s
3. time to empty the container is 20/27 hr
4. time to empty the container is 27/20 hr

Correct answer: speed of efflux when height of liquid is 0.2 m is 2 m/s

Solution

v=sqrt(2gh): at h=0.8m v=4 m/s (A wrong); at h=0.2m v=2 m/s (B correct). Time integration gives T=8*pi*sqrt(2)/(A0*sqrt(20)*3)=8000/3 s=20/27 hr (C correct). Answer: B and C.

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