Bottom of a cylindrical vessel has a hole of area $A$. If water is filled up to a height $h$, it flows out in $t$ seconds. If water is filled to a height $4 h$, it will flow out in time

• A

  $t$
• B

  $4 t$
• Correct answer
  C

  $2 t$
• D

  $\frac{t}{4}$

Solution

$$ \text { The given situation is shown in the figure, } $$
Time taken to flow out of water upto height $h$ from hole completely, $$ t=\sqrt{\frac{2 h}{g}} $$ When, $\quad h^{\prime}=4 h$, then $$ t^{\prime}=\sqrt{\frac{2 h^{\prime}}{g}}=\sqrt{\frac{2 \times 4 h}{g}}=2 \sqrt{\frac{2 h}{g}}=2 t $$ [from Eq. (i)]

Hence, the correct answer is option: 'C'.