Woopsie, there was a typo in the earlier post.
##a = 0## gives ##- \pi \rho_{w} g \cdot \frac{4}{3}R^{3}## which seems right.
## a = R ## gives ## \pi \rho_{w} g R^{2} h - \frac{2}{3} \pi R^{3} \rho_{w} g ## which also seems right
Positive indicates a downward force.
Yay! sanity checks are...
Thanks everyone.
I went through the calculations again .. checking each and every line and voila the culprit was that I missed a factor of 2.
Just for completeness, I get the force by the liquid (curved area) to be ##\displaystyle \pi \rho _{w} g \left [ a^{2} h - \frac{1}{3} \left ( a^{2}...
@SteamKing
For the first method, I can calculate the volume. What I intend to find out is the force exerted by the liquid on the curved section of the hypothetical ball (which will be the answer as needed for the original question). Since the buoyant force force for the hypothetical case is...
Homework Statement
There is a cylindrical container that has a small hole of radius ##a ( < R)## at the bottom. A sphere of radius ##R## and density ##\rho_{s} > \rho_{w}## is placed in the cylinder such that it completely covers the hole (a part of it sticks out as in attached figure). The...
For the energy method
U = \frac{1}{2\mu _{o}}\int B^{2}dV
=> U = \frac{1}{2\mu _{o}} \int \frac{\mu _{o}^{2}s^{2}}{4\pi ^{2}a^{4}}sdsd\phi dz
phi varies from 0 to 2pi, s from 0 to a and integral of dz = l
equating value of U with 0.5LI^2 we get
L_{perunitlength} = \frac{\mu...
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Homework Statement
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