Question

A wooden stick of length $l$, and radius $R$ and density $\rho$ has a small metal piece of mass $m$(of negligible volume) attached to its one end. Find the minimum value for the mass $m$ (in terms of given parameters) that would make the stick float vertically in equilibrium in a liquid of density $\sigma (>\rho )$.

Answer 1

For the road to float in liquid at equilibrium

gravitational mass = Buoyant force

$(mg+\rho vg)=\sigma Vg$

$m+\rho v=\sigma V$

here $V=\pi R^{2}l$

$m=(\sigma -\rho )\pi R^{2}l$

minimum value of m is $(\sigma -\rho )\pi R^{2}l$.