A cylindrical container has radius 40 cm and volume 528 \((\text{dm}^3)\). It is placed on a table of same height as of container. A hole is made 70 cm below from the free surface. Find range of efflux on ground if the container is filled completely.
Show Hint
Use Torricelli’s law for calculating the velocity of efflux and the range of the efflux when dealing with liquids flowing out of a hole in a container.
The formula for volume is given by:
\[
V = \pi r h
\]
Substitute the given values:
\[
528 \times 10^3 = \frac{22}{7} \times (40)^2 \times h
\]
Simplify for \( h \):
\[
h = \frac{528 \times 10^3 \times 7}{22 \times 40^2} = 105 \, \text{cm}
\]
Now, for the time \( t \), use the formula:
\[
t = \sqrt{\frac{2H}{g}}
\]
Substitute the values:
\[
t = \sqrt{\frac{2 \times 140 \times 10^{-2}}{10}} = \sqrt{28 \times 10^{-1}} = \sqrt{2.8}
\]
Now, for the resistance \( R \):
\[
R = ut = \sqrt{2 \times 10 \times 70 \times 10^{-2}} \times \sqrt{28 \times 10^{-1}}
\]
Simplify further:
\[
R = \sqrt{14 \times 28 \times 10^{-1}} = 14 \sqrt{2} \times 10^{-1} = 140 \, \text{cm}
\]
Thus, the final value for \( R \) is \( 140 \, \text{cm} \).
