A bucket contains water filled upto a height $=$ $15 cm$. The bucket is tied to a rope which is passed over a frictionless light pulley and the other end of the rope is tied to a weight of mass which is half of that of the (bucket $+$ water). The water pressure above atmosphere pressure at the bottom is ....... $kPa$

Two bodies having volumes $V$ and $2V $ are suspended from the two arms of a common balance and they are found to balance each other. If larger body is immersed in oil (density $d_1 $ $=$ $ 0.9$ $ gm/cm^3$) and the smaller body is immersed in an unknown liquid, then the balance remain in equilibrium. The density of unknown liquid is given by ......... $gm/cm^3$

A triangular lamina of area $A$ and height h is immersed in a liquid of density $\rho $ in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is

A barometer kept in an elevator reads $76 \,cm$ when the elevator is accelerating upwards. The most likely pressure inside the elevator (in $cm$ of $Hg$ ) is ........

A barometer kept in an elevator reads $76 \,cm$ when it is at rest. If the elevator goes up with some acceleration, the reading will be .......... $cm$

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta=45^{\circ} . P_1$ and $P_2$ are pressures at points 1 and 2 , respectively, located at the base of the tube. Let $\beta=\left(P_1-P_2\right) /(\rho g d)$, where $\rho$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity. Which of the following statement($s$) is(are) correct?

$(A)$ $\beta=0$ when $a= g / \sqrt{2}$

$(B)$ $\beta>0$ when $a= g / \sqrt{2}$

$(C)$ $\beta=\frac{\sqrt{2}-1}{\sqrt{2}}$ when $a= g / 2$

$(D)$ $\beta=\frac{1}{\sqrt{2}}$ when $a= g / 2$