Question:
A rectangular vessel when full of water takes 10 min to be emptied through an orifice in its bottom. How much time will it take to be emptied, when half filled with water?
A rectangular vessel when full of water takes 10 min to be emptied through an orifice in its bottom. How much time will it take to be emptied, when half filled with water?
Show Hint
Emptying time of tank is proportional to square root of height of liquid.
Updated On: Apr 15, 2026
- 4 min
- 6 min
- 7 min
- 8 min
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
From Torricelli’s law:
\[
v = \sqrt{2gh}
\]
Time to empty tank:
\[
t \propto \sqrt{h}
\]
Step 1: Relation.
\[ t \propto \sqrt{h} \] For full height \(H\): \[ t_1 \propto \sqrt{H} = 10 \] For half height: \[ t_2 \propto \sqrt{\frac{H}{2}} = \frac{10}{\sqrt{2}} = 7 \]
Step 1: Relation.
\[ t \propto \sqrt{h} \] For full height \(H\): \[ t_1 \propto \sqrt{H} = 10 \] For half height: \[ t_2 \propto \sqrt{\frac{H}{2}} = \frac{10}{\sqrt{2}} = 7 \]
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