$A$ large tank is filled with water to a height $H$. $A$ small hole is made at the base of the tank. It takes $T_1$ time to decrease the height of water to $H/\eta$ (where $\eta > 1$),and it takes $T_2$ time to drain the rest of the water. If $T_1 = T_2$,then the value of $\eta$ is:

$A$ person in a lift is holding a water jar,which has a small hole at the lower end of its side. When the lift is at rest,the water jet coming out of the hole hits the floor of the lift at a distance $d$ of $1.2 \ m$ from the person. In the following,the state of the lift's motion is given in List-$I$ and the distance where the water jet hits the floor of the lift is given in List-$II$. Match the statements from List-$I$ with those in List-$II$ and select the correct answer using the code given below the lists.

List-$I$	List-$II$
$P$. Lift is accelerating vertically up.	$1$. $d = 1.2 \ m$
$Q$. Lift is accelerating vertically down with an acceleration less than the gravitational acceleration.	$2$. $d < 1.2 \ m$
$R$. Lift is moving vertically up with constant speed.	$3$. $d > 1.2 \ m$
$S$. Lift is falling freely.	$4$. No water leaks out of the jar.

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to zero is

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to $0$ is

$A$ container is filled with water up to a height $h$. $A$ small hole is made at the bottom. What is the ratio of the time taken for the water level to fall from $h$ to $\frac{h}{2}$ to the time taken for it to fall from $\frac{h}{2}$ to $0$?

$A$ cylindrical vessel of cross-sectional area $1000 \ cm^2$ is fitted with a frictionless piston of mass $10 \ kg$ and filled with water completely. $A$ small hole of cross-sectional area $10 \ mm^2$ is opened at a point $50 \ cm$ deep from the lower surface of the piston. The velocity of efflux from the hole will be ........... $m/s$.