A cubical block of steel of side 'a ' and density 'p'floats on mercury of density with a part of it being submerged. The height of the block above the Mercury level is given by
a * [1 - (p / density of Hg)]
To determine the height of the steel block above the mercury level, we can use the principle of buoyancy.
Buoyancy is the upward force exerted on an object immersed in a fluid, in this case, mercury. It depends on the density of the fluid and the volume of the submerged part of the object.
In this scenario, the steel block floats on mercury, which means it experiences an upward buoyant force equal to its weight. The weight of the block is given by its mass multiplied by gravity (W = m * g).
To find the mass of the steel block, we need to know its volume and density. Since the block is a cube with side 'a', its volume is given by V = a * a * a = a^3. The density of the steel block is given as 'p'.
So, the mass of the steel block can be calculated as m = p * V = p * (a^3).
The buoyant force acting on the steel block is equal to the weight of the mercury displaced by the submerged part of the block. The volume of the displaced mercury is equal to the submerged volume of the block.
The submerged volume of the block can be found by multiplying the height of the submerged portion by its cross-sectional area, which is a * a = a^2.
Let's assume the height of the submerged portion is 'h'. Therefore, the submerged volume is V_submerged = a^2 * h.
The buoyant force can be calculated as F_buoyant = density_of_mercury * gravity * V_submerged. Since the density of mercury is given as 'd_mercury', the buoyant force becomes F_buoyant = d_mercury * g * (a^2 * h).
According to the principle of buoyancy, the buoyant force is equal to the weight of the steel block, so we have:
d_mercury * g * (a^2 * h) = p * (a^3) * g.
Now, we can solve for 'h' to obtain the height of the block above the mercury level:
h = (p * (a^3))/(d_mercury * a^2).
Simplifying, we get:
h = p * (a/d_mercury).
Therefore, the height of the block above the mercury level is given by h = p * (a/d_mercury).