An inverted U-tube manometer is used to measure the pressure difference between two pipes $$A$$ and $$B,$$ as shown in the figure. Pipe $$A$$ is carrying oil (specific gravity $$= 0.8$$) and pipe $$B$$ is carrying water. The densities of air and water are $$1.16\,\,kg/{m^3}$$ and $$1000\,\,kg/{m^3},$$, respectively. The pressure difference between pipes $$A$$ and $$B$$ is _______________$$kPa.$$

$$Acceleration$$ $$due$$ $$to$$ $$gravity$$ $$g = 10\,m/{s^2}$$

For a floating body, buoyant force acts at the

A plastic sleeve of outer radius $${r_0} = 1\,\,mm$$ covers a wire (radius $$r = 0.5$$ $$mm$$) carrying electric current. Thermal conductivity of the plastic is $$0.15\,\,W/m$$-$$K$$. The heat transfer coefficient on the outer surface of the sleeve exposed to air is $$25$$ $$W/{m^2}$$-$$K$$. Due to the addition of the plastic cover, the heat transfer from the wire to the ambient will

A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ by immersing it in a water environment at $$300$$ $$K.$$ The convective heat transfer coefficient is $$1000\,\,W/{m^2}$$-$$K.$$ Thermal conductivity of steel is $$40$$ $$W/m$$-$$K.$$ The time constant for the cooling process $$\tau $$ is $$16s.$$ The time required (in $$s$$) to reach the final temperature is __________________.