A sphere of relative density $$\sigma$$ and diameter $$D$$ has concentric cavity of diameter $$d$$. The ratio of $$\frac{D}{d}$$, if it just floats on water in a tank is :

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9):

Young's modulus is determined by the equation given by $$\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2}$$ where $$M$$ is the mass and $$l$$ is the extension of wire used in the experiment. Now error in Young modules $$(Y)$$ is estimated by taking data from $$M-l$$ plot in graph paper. The smallest scale divisions are $$5 \mathrm{~g}$$ and $$0.02 \mathrm{~cm}$$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $$500 \mathrm{~g}$$ and $$2 \mathrm{~cm}$$ respectively then percentage error of $$Y$$ is :

Correct Bernoulli's equation is (symbols have their usual meaning) :