Calculate the rise in water level for Question 1.

Step 1: Calculate the rise in water level for Question 1. The volume of the metal cube is V_cube = 10^3 mm^3. The cross-sectional area of the cylinder is A_cylinder = 1.5 × 10^2 mm^2. When the cube is lowered into the cylinder, it displaces a volume of water equal to its own volume. This displaced volume causes the water level to rise. The volume of displaced water can be expressed as V_displaced = A_cylinder × h, where h is the rise in water level. Therefore, V_cube = A_cylinder × h. 10^3 mm^3 = (1.5 × 10^2 mm^2) × h h = 10^3 mm^31.5 × 10^2 mm^2 h = 1000 mm^3150 mm^2 h = (100)/(15) mm h = (20)/(3) mm h ≈ 6.67 mm This matches option A, 6.67 × 10^0 mm. The water level rises by 6.67 mm. Step 2: Calculate the radius of the cylinder for Question 2. The radius of the spherical metal bob is r_bob = 3 cm. The water level rises by h = 1 cm. The volume of the spherical bob is given by V_sphere = (4)/(3) r_bob^3. The volume of water displaced in the cylinder is given by V_displaced = R_cylinder^2 h, where R_cylinder is the radius of the cylinder. Since the bob is fully immersed, the volume of displaced water is equal to the volume of the bob: V_sphere = V_displaced (4)/(3) r_bob^3 = R_cylinder^2 h Substitute the given values: (4)/(3) (3 cm)^3 = R_cylinder^2 (1 cm) Divide both sides by : (4)/(3) (27 cm^3) = R_cylinder^2 (1 cm) 4 × 9 cm^3 = R_cylinder^2 (1 cm) 36 cm^3 = R_cylinder^2 (1 cm) R_cylinder^2 = 36 cm^31 cm R_cylinder^2 = 36 cm^2 R_cylinder = sqrt(36 cm)^2 R_cylinder = 6 cm The radius of the cylinder is 6 cm. Step 3: Identify the principle for Question 3. The principle of the transmissibility of pressure in a fluid at rest in all directions is known as Pascal's Law. Pascal's Law states that a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. The correct answer is D. Pascal's Law. Step 4: Identify the incorrect statement about liquid pressure for Question 4. Let's analyze each statement: A. At a point in a liquid is proportional to the depth (P = g h). This statement is correct*. B. At any point in a liquid is the same at the same level. This statement is correct*. C. Is exerted equally in all directions at any point. This statement is correct* (a consequence of Pascal's Law). D. At a particular depth depends on the shape of the vessel. This statement is incorrect*. Liquid pressure at a given depth depends only on the density of the liquid, the acceleration due to gravity, and the depth, not on the shape or volume of the container. The statement that is NOT correct is D. At a particular depth depends on the shape of the vessel. Step 5: Calculate the height of the atmosphere for Question 5. Given: • Normal atmospheric pressure, P = 10^5 Nm^-2. • Acceleration due to gravity, g = 10 ms^-2. • Uniform density of the atmosphere, = 1 kgm^-3. The formula for hydrostatic pressure is P = g h, where h is the height. Rearrange the formula to solve for h: h = (P)/( g) Substitute the given values: h = 10^5 Nm^-2(1 kgm^-3)(10 ms^-2) h = 100000 Nm^-210 kgm^-2s^-2 h = 10000 m The height of the atmosphere is 10 000 m.