question_answer

A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius ‘a’. The time in which it will be emptied is:                                                                      [JEE ONLINE 12-04-2014]

A)  \[\frac{2A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\] 

B)       \[\frac{\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]

C)  \[\frac{2\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]  

D)       \[\frac{A}{\sqrt{2}\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]

Correct Answer: B

Solution :

[b] Let the rate of falling water level be

Initially at t = 0 ; h = h

t = t ; h = 0

Then,

[velocity of efflux of liquid ]

Integrating both sides