A piece of cork starts from rest at the bottom of a lake and floats up. Its velocity $v$ is plotted against time $t.$ Which of the following best represents the resulting curve-

A sealed tank containing a liquid of density $\rho$ moves with a horizontal acceleration $a,$ as shown in the figure. The difference in pressure between the points $A$ and $B$ is-

The $U$-tube shown has a uniform cross-section. A liquid is filled in the two arms up to heights $h_1$ and $h_2,$ and then the liquid is allowed to move. Neglect viscosity and surface tension. When the levels equalize in the two arms, the liquid will-

Water coming out of the mouth of a tap and falling vertically in streamline flow forms a tapering column, i.e., the area of cross-section of the liquid column decreases as it moves down. Which of the following is the most accurate explanation for this:-

There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to-

A homogeneous solid cylinder of length $L(L<\frac{H}{2}),$ cross-sectional area $\frac{A}{5}$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $\frac{L}{4}$ in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure $P_0.$ Then, density $D$ of solid is given by :-

A mercury manometer is connected as shown in the figure. The difference in height $\Delta h$ is : (symbols have usual meaning).

An open pan P filled with water (density ${\rho }_w$ ) is placed on a vertical rod, maintaining equilibrium. A block of density $\rho$ is placed on one side of the pan as shown. Water depth is more than height of the block.