Search any question & find its solution
Question:
Answered & Verified by Expert
The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to
Options:
Solution:
1305 Upvotes
Verified Answer
The correct answer is:
Radius of the vessel
Pressure at the bottom $=h \rho g$
and pressure on the vertical surface $=\frac{1}{2} h \rho g$
Now, according to problem
Force at the bottom = Force on the vertical surface
$\Rightarrow{ }^{h \rho g \times \pi r^2=\frac{1}{2} h \rho g \times 2 \pi \cdot h} \Rightarrow h=r$
and pressure on the vertical surface $=\frac{1}{2} h \rho g$
Now, according to problem
Force at the bottom = Force on the vertical surface
$\Rightarrow{ }^{h \rho g \times \pi r^2=\frac{1}{2} h \rho g \times 2 \pi \cdot h} \Rightarrow h=r$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.