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 _______________$$kPa.$$

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

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that $$45$$ percent of its volume is in oil while the rest is in water. The density of the body is _______________ $$kg/{m^3}.$$

The specific gravity of oil is $$0.7$$ and density of water is $$1000$$ $$kg/{m^3}.$$

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