A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm and length = 8 m) is immersed in the water and is hinged without friction at point A on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = 11.4) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod.

Assume density of water = 10³ kg/m³ and π = 3.14.

Radius of the ball is _______ cm (round off to 2 decimal places).

For the stability of a floating body the

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 _______________$$kPa.$$

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

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $$2R \times L$$ at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius $$R.$$ The tank is filled with a liquid of density $$\rho $$ up to the tip of the plug. The gravitational acceleration is $$g.$$ Neglect the effect of the atmospheric pressure.

The force $$F$$ required to hold the plug in its position is