$A$ liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis,the liquid rises at its sides. If the radius of the vessel is $0.05\, m$ and the speed of rotation is $2$ revolutions per second,the difference in the heights of the liquid at the centre and at the sides of the vessel will be ...... $cm$. (Take $g = 10\, ms^{-2}$ and $\pi^2 = 10$)

$A$ 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 $\beta=(P_1-P_2) / (\rho g d)$,where $\rho$ is the 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 $a=g / 2$

$A$ river of salty water is flowing with a velocity $2 \,m/s$. If the density of the water is $1.2 \,g/cc$, then the kinetic energy of each cubic metre of water is

$A$ piece of metal weighs $46 \, g$ in air. When it is immersed in a liquid of specific gravity $1.24$ at $27^{\circ}C$,it weighs $30 \, g$. When the temperature of the liquid is raised to $42^{\circ}C$,the metal piece weighs $30.5 \, g$ and the specific gravity of the liquid at $42^{\circ}C$ is $1.20$. Calculate the coefficient of linear expansion of the metal.

If the heart pushes $1 \ cc$ of blood in one second under pressure $20000 \ N/m^2$,the power of the heart is ....... $W$.

$A$ razor-blade floats on the surface of water contained in a glass. When the glass is gently shaken,the razor-blade sinks. Mark the incorrect statement.