Question 450: Properties of Matter

Question

A wooden cylinder of diameter $4 r$, height $h$ and density $\frac{\rho}{3}$ is kept on a hole of diameter $2 r$ of a tank, filled with water of density $\rho$ as shown in the figure. The height of the base of cylinder from the base of tank is H .

Accepted Answer

$$ \begin{aligned} & \pi r^2=	ext { Area of base of cylinder in air } \ & 3 \pi r^2=	ext { Area of base of cylinder in water. } \ & 4 \pi r^2=	ext { Cross-sectional area of the cylinder. } \end{aligned} $$
$$ \begin{aligned} &	ext { Equating the forces, we get }\ &\begin{aligned} & {\left[\mathrm{P}_0+ho g h_1ight] \pi\left(4 r^2ight)+\left(\frac{ho}{3}ight) \pi r^2 .4 h g} \ & =\left[\mathrm{P}_0+ho g\left(h_1+hight)ight] \pi\left(3 r^2ight)+\mathrm{P}_0 \pi r^2 \ & ho g h_1 \cdot 4 \pi r^2+\frac{ho g h 4 \pi r^2}{3}=ho g h_1 3 \pi r^2+ho h g 3 \pi r^2 \ & ho g h_1 \pi r^2=ho g h \pi r^2\left(3-\frac{4}{3}ight) \ & h_1=h\left(\frac{5}{3}ight) \end{aligned} \end{aligned} $$

Answer

$\frac{2 h}{3}$

Answer

$\frac{5 h}{4}$

Answer

$\frac{5 h}{3}$

Answer

$\frac{5 h}{2}$

Properties of Matter

A wooden cylinder of diameter 4 r, height h and density \frac{\rho}{3} is kept on a hole of diameter 2 r of a tank, filled with water of density \rho as shown in the figure. The height of the base of cylinder from the base of tank is H .

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