Question

A water tank of height 10 m, completely filled with water is placed on a level ground. It has two holes one at 3 m and the other at 7 m from its base. The water ejecting from

• A. both the holes will fall at the same spot
• B. upper hole will fall farther than that from the lower hole
• C. upper hole will fall closer than that from the lower hole
• D. more information is required

Answer 1

Answer: (A)

Speed of water from hole $=\sqrt{2 g h}$
Let the time taken to fall to ground $=t$
Using, $S=u t+\frac{1}{2} a t^{2}$
$(H-h)=\frac{1}{2} g t^{2}$
$t=\sqrt{\frac{2(H-h)}{g}}$

$x=\sqrt{2 g h} \cdot t=\sqrt{4(H-h) \cdot h}$
Here, $H=10 \,m , h_{1}=3 m , h_{2}=+7 \,m$
$x_{1}=2 \sqrt{(10-3) \times 3}$
$x_{2}=2 \sqrt{(10-7) \times 7}$
$ \Rightarrow x_{1}=x_{2}$