Posted by sand on Monday, December 26, 2011 at 11:44am.
You need to know the specific gravity (or density) of both lead and mercury to answer this question.
Lead has a specific gravity of 11.35, so it is 11.35 times as dense as water. It's density in SI units is
rho1 = 11.35*10^3 kg/m^3
Mercury has a specific gravity of 13.56 and density
rho2 = 13.56*10^3 kg/m^3
The buoyancy force is (rho2)*g*V'
where V' is the displaced volume of mercury. The brick's weight is W = (rho1*g*V)
where V is the volume of the brick.
Setting them equal,
V' = (rho1/rho2)*V = 0.837
The fraction above the surface must be 0.163 or 16.3%
To hold it all beneath the surface, the force required is (rho2 - rho1)*g*V =
2.21*10^3*9.8*7*10^-4 = 15.2 N
Thanks a lot
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