Question:
A cylindrical vessel of \(40\,\text{cm}\) radius is completely filled with water and its capacity is \(528\,\text{dm}^3\) (\(\text{dm}=\text{decimetre}\)). The vessel is placed on a solid block of same height as vessel. If a small hole is made at \(70\,\text{cm}\) below the top of water level, then the horizontal range of water falling on the ground in the beginning is ______ cm.
A cylindrical vessel of \(40\,\text{cm}\) radius is completely filled with water and its capacity is \(528\,\text{dm}^3\) (\(\text{dm}=\text{decimetre}\)). The vessel is placed on a solid block of same height as vessel. If a small hole is made at \(70\,\text{cm}\) below the top of water level, then the horizontal range of water falling on the ground in the beginning is ______ cm.
Updated On: Apr 12, 2026
- \(120\sqrt2\)
- \(140\sqrt2\)
- \(140\sqrt3\)
- \(120\sqrt3\)
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The Correct Option is A
Solution and Explanation
Concept:
For a small hole in a tank, velocity of efflux is given by Torricelli’s theorem:
\[
v=\sqrt{2gh}
\]
where \(h\) is the height of water above the hole.
The horizontal range when water falls from height \(H\) is
\[
R=v\sqrt{\frac{2H}{g}}
\]
Step 1: {Find the height of the cylindrical vessel.}
Volume of cylinder:
\[
V=\pi r^2 h
\]
Given:
\[
V=528\,\text{dm}^3 = 528\times1000 = 528000\,\text{cm}^3
\]
\[
r=40\,\text{cm}
\]
\[
528000=\pi(40)^2h
\]
\[
528000=1600\pi h
\]
Using \( \pi=\frac{22}{7} \):
\[
h=105\,\text{cm}
\]
Step 2: {Determine vertical heights.}
Hole is \(70\,\text{cm}\) below the water surface.
Thus
\[
h=70\,\text{cm}
\]
Height of hole above ground:
\[
H=105-70=35\,\text{cm}
\]
But vessel is placed on a block of same height \(105\,\text{cm}\):
\[
H=105+35=140\,\text{cm}
\]
Step 3: {Find the range.}
\[
R=2\sqrt{hH}
\]
\[
=2\sqrt{70\times140}
\]
\[
=2\sqrt{9800}
\]
\[
=120\sqrt2
\]
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