$9\  kg$ of mercury is poured into a glass $U-tube$ with inner diameter of $1.2 \ cm$. The mercury can flow without friction within the tube.  the oscillation period ......... $\sec$. Density of mercury = $13.6 × 10^3\  kg/m^3$. 

Figure shows two containers $P$ and $Q$ with same base area $A$ and each filled upto same height with same liquid. Select the correct alternative .............

Radius of an air bubble at the bottom of the lake is $r$  and it becomes $ 2r $ when the air bubbles rises to the top surface of the lake. If $P $ $cm$  of water be the atmospheric pressure, then the depth of the lake is

A container of height $10\, cm$ is filled with water. There is a hole at bottom. Find the pressure difference between points at top and bottom.

A square gate of size $1\,m \times 1\,m$ is hinged at its mid-point. A fluid of density $\rho$ fills the space to the left of the gate. The force F required to hold the gate stationary is

Consider the wall of a dam to be straight with height $H$ and length $L$. It holds a lake of water of height $h (h < H)$ on one side. Let the density of water be $\rho_{ w }$. Denote the torque about the axis along the bottom length of the wall by $\tau_1$. Denote also a similar torque due to the water up to height $h / 2$ and wall length $L / 2$ by $\tau_2$. Then $\tau_1 / \tau_2$ (ignore atmospheric pressure) is