A rectangular vessel when full of water takes 10 minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water

Options

A. 9 min
B. 7 min
C. 5 min
D. 3 min

Answer

B

Explanation

If `A_(0)` is the area of orifice at the botton below the free surface and A thhat of vessel time t taken to the empired the tank
`t=(A)/(A_(0))sqrt((2H)/(g))`
`therefore(t_(1))/(t_(2))=sqrt((H_(1))/(H_(2)))`
`implies(t)/(t_(2))=sqrt((H_(1))/(H_(1)//2))`
`implies(t)/(t_(2))=sqrt(2)`
`thereforet_(2)=(t)/(sqrt(2))=(10)/(sqrt(2))=5sqrt2`
`~~7`min