Properties Of Solids And Liquids Question 231
Question: A cylindrical vessel of 90 cm height is kept filled upto the brim. It has four holes 1, 2, 3, 4 which are respectively at heights of 20 cm, 30 cm, 45 cm and 50 cm from the horizontal floor PQ. The water falling at the maximum horizontal distance from the vessel comes from[CPMT 1989]
Options:
A) $ x=\sqrt{D(H-D)} $
B) $ x=\sqrt{\frac{D(H-D)}{2}} $
C) $ x=2\sqrt{D(H-D)} $
D) $ x=4\sqrt{D(H-D)} $
Show Answer
Answer:
Correct Answer: C
Solution:
Time taken by water to reach the bottom= $ t=\sqrt{\frac{2(H-D)}{g}} $
and velocity of water coming out of hole, $ v=\sqrt{2gD} $
Horizontal distance covered $ x=v\times t $ = $ \sqrt{2gD}\times \sqrt{\frac{2(H-D)}{g}} $ = $ 2\sqrt{D(H-D)} $
