Pressure due to a fluid column and Pascal's law — practice questions

Question 1 · difficulty L2 · understanding

A cubical block of density $\rho_b=600 \mathrm{~kg} / \mathrm{m}^3$ floats in a liquid of density $\rho_{\mathrm{e}}=900 \mathrm{kg} / \mathrm{m}^3$. If the height of block is $H=8.0 \mathrm{~cm}$ then height of the submerged part is $\_\_\_\_$ cm .

• A. 6.3
• B. 4.3
• C. 7.3
• D. 5.3

Question 2 · difficulty L2 · understanding

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg m -3 )

• A. 400 cm 3
• B. 600 cm 3
• C. 1400 cm 3
• D. 4000 cm 3

Question 3 · difficulty L2 · understanding

Given below are two statements: Statement I : Pressure in a reservoir of water is same at all points at the same level of water. Statement II : The pressure applied to enclosed water is transmitted in all directions equally. In the light of the above statements, choose the correct answer from the options given below:

• A. Both Statement I and Statement II are false
• B. Statement I is false but Statement II is true
• C. Statement I is true but Statement II is false
• D. Both Statement I and Statement II are true

Question 4 · difficulty L2 · understanding

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$ Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed. Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. In the light of the above statements, choose the most appropriate answer from the options given below

• A. Both A and R are correct but R is NOT the correct explanation of A
• B. A is not correct but R is correct
• C. A is correct but R is not correct
• D. Both A and B are correct and R is the correct explanation of A

Question 5 · difficulty L2 · understanding

A bicycle tyre is filled with air having pressure of $$270 ~\mathrm{kPa}$$ at $$27^{\circ} \mathrm{C}$$. The approximate pressure of the air in the tyre when the temperature increases to $$36^{\circ} \mathrm{C}$$ is

• A. 262 kPa
• B. 360 kPa
• C. 270 kPa
• D. 278 kPa

Question 6 · difficulty L2 · understanding

A pressure-pump has a horizontal tube of cross sectional area $$10 \mathrm{~cm}^{2}$$ for the outflow of water at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is : [given: density of water $$=1000 \mathrm{~kg} / \mathrm{m}^{3}$$]

• A. 300 N
• B. 500 N
• C. 250 N
• D. 400 N

Question 7 · difficulty L2 · understanding

An object is located at 2 km beneath the surface of the water. If the fractional compression $${{\Delta V} \over V}$$ is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm $$-$$3 and g = 9.8 ms $$-$$2 ]

• A. 1.44 $$\times$$ 10 7 Nm $$-$$2
• B. 1.44 $$\times$$ 10 9 Nm $$-$$2
• C. 1.96 $$\times$$ 10 7 Nm $$-$$2
• D. 2.26 $$\times$$ 10 9 Nm $$-$$2

Question 8 · difficulty L2 · understanding

The pressure acting on a submarine is 3 $$\times$$ 10 5 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : (Assume that atmospheric pressure is 1 $$\times$$ 10 5 Pa density of water is 10 3 kg m $$-$$3 , g = 10 ms $$-$$2 )

• A. $${{200} \over 5}$$%
• B. $${{200} \over 3}$$%
• C. $${{3} \over 200}$$%
• D. $${{5} \over 200}$$%

Question 9 · difficulty L2 · understanding

A tub is filled with water and a wooden cube $10\ \text{cm} \times 10\ \text{cm} \times 10\ \text{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by $3.87$ cm. The mass of the metal coin is ________ gram. (Take water density as $1\ \text{g/cm}^3$ and density of wood as $0.4\ \text{g/cm}^3$)

Question 10 · difficulty L2 · understanding

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100 \mathrm{~cm}^2$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$. What force one needs to apply on the hinged door so that it does not get opened ? $$\text { (Acceleration due to gravity }=10 \mathrm{~m} / \mathrm{s}^2 \text { ) }$$