Mechanical Prop...

A small rain droplet is falling with terminal speed $$\upsilon$$. Terminal speed of another droplet of radius twice the radius of first droplet will be :

The mercury columns in a manometer are given as 2$$\mathrm { cm }$$ and 12$$\mathrm { cm }$$ respectively. Specific gravity of mercury is13.6. The gauge pressure is pressure is $$\left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right)$$

Two tubes of radii $$r_1$$ and $$r_2$$, and length $$l_1$$ and $$l_2$$ respectively, are connected in series and a liquid flows through each of them in streamline conditions. $$P_1$$ and $$P_2$$ are pressure differences across the two tubes. If $$P_2$$ is $$4P_1$$ and $$l_2$$ is $$\frac {l_1}{4}$$, then the radius $$r_2$$ will be equal to :

The terminal speed $$\upsilon$$ of a rain water drop in air is :

The area of cross section of the wider tube shown in figure is 900 $$
\mathrm{cm}^{2}
 $$. If the boy standing on the piston weighs 45 kg, the difference in the levels of water in the two tubes.

Consider a wooden block immersed in a beaker containing water. If the beaker now starts accelerating upwards then :

A block of wood of length $$50\ cm$$ and area of cross-section $$10\ cm^{2}$$, floats in water with $$\dfrac{3}{5}$$ of its lengths above water. Calculate weight of wood 

A $$0.50\ L$$ container is occupied by nitrogen at a pressure of $$800\ torr$$ and a temperature of $$0^{o}C$$. The container can only withstand a pressure of $$3.0\ atm$$. What is the highest temperature $$(^{o}C)$$ to which the container may be heated?

Water enters a horizontal pipe of non uniform cross section with a velocity
of $$0.4 \mathrm { ms } ^ { - 1 }$$ and leaves the other end with a velocity of 0.6$$\mathrm { ms } ^ { - 1 } .$$ Pressure of water at the first end is $$1500 \mathrm { Nm } ^ { - 2 } ,$$ then pressure at the other end is