A homogeneous solid cylinder of length L(L<H/2) . Cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure ${\mathrm{P}}_0$. Then density D of solid is given by

(1) $\frac{5}{4}\mathrm{d}$   
                 
(2) $\frac{4}{5}\mathrm{d}$

(3) $\mathrm{d}$     
                   
(4) $\frac{d}{5}$

 A wooden block with a coin placed on its top, floats in water as shown in fig. The distance \(l\) and \(h\) are shown there. After some time the coin falls into the water. Then:
                      

A block of ice floats on a liquid of density 1.2 $g/c{m}^3$ in a beaker. Then level of liquid when ice completely melts-

(1) Remains same                         

(2) Rises

(3) Lowers                                   

(4) (a), (b) or (c)

A vessel of area of cross-section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from ${\mathrm{H}}_1$ to ${\mathrm{H}}_2$ will be

(1)$\frac{\mathrm{A}}{\mathrm{a}}\sqrt{\frac{2}{\mathrm{g}}}\left[\sqrt{{\mathrm{H}}_1}-\sqrt{{\mathrm{H}}_2}\right]$             

(2) $\sqrt{2\mathrm{gh}}$

(3) $\sqrt{2\mathrm{gh}({\mathrm{H}}_1-{\mathrm{H}}_2)}$                     

(4) $\frac{\mathrm{A}}{\mathrm{a}}\sqrt{\frac{g}{2}}\left[\sqrt{{\mathrm{H}}_1}-\sqrt{{\mathrm{H}}_2}\right]$

A lead shot of 1mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by

Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by

From amongst the following curves, which one shows the variation of the velocity v with time t for a small sized spherical body falling vertically in a long column of a viscous liquid -

A liquid does not wet the sides of a solid if the angle of contact is

(1) Zero                                     

(2) Obtuse (More than 90°)

(3) Acute (Less than 90°)           

(4) 90°

The meniscus of mercury in the capillary tube is

(1) Convex           

(2) Concave

(3) Plane               

(4) Uncertain

At which of the following temperatures, the value of surface tension of water is minimum ?

(1) $4°\mathrm{C}$                                       

(2) $25°\mathrm{C}$

(3) $50°\mathrm{C}$                                     

(4) $75°\mathrm{C}$