Home
Class 12
PHYSICS
A: Stoke's formula for viscous drag is n...

A: Stoke's formula for viscous drag is not really valid for oil -drops of extremely minute sizes.
R: Stoke's formula is valid for motion through a homogeneous continuous medium and the size of the drop should be much larger than the intermolecular separation in the medium for this assumption to be valid.

A

If both Assertion & Reason are true and the reason is the correct explantion of the assertion , then mark (1)

B

if both Assertion & Reason are true but the reason is not the correct explantion of the assertion , then mark (2)

C

If Assertion is true statement but Reason is false, then mark (3)

D

If both Assertion and Reason are false statements, then mark (4)

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given statements A and R, we need to evaluate their validity based on the principles of physics, particularly focusing on Stoke's formula and the conditions under which it applies. ### Step-by-Step Solution: 1. **Understanding Stoke's Formula**: - Stoke's formula describes the viscous drag force experienced by a sphere moving through a viscous fluid. The formula is given by: \[ F = 6 \pi \eta r v \] where \( F \) is the drag force, \( \eta \) is the dynamic viscosity of the fluid, \( r \) is the radius of the sphere, and \( v \) is the velocity of the sphere. 2. **Conditions for Stoke's Formula Validity**: - Stoke's formula is valid under certain conditions: - The fluid must be a homogeneous continuous medium. - The size of the sphere (or drop) must be much larger than the intermolecular distances in the fluid. - The flow must be laminar, meaning that the Reynolds number should be low (typically less than 1). 3. **Evaluating Assertion (A)**: - The assertion states that Stoke's formula is not valid for oil drops of extremely minute sizes. This is true because: - For very small droplets, the effects of molecular interactions become significant, and the assumptions of a continuous medium break down. - Therefore, the assertion (A) is **true**. 4. **Evaluating Reason (R)**: - The reason states that Stoke's formula is valid for motion through a homogeneous continuous medium and that the size of the drop should be much larger than the intermolecular separation in the medium for this assumption to hold. - This statement accurately describes the conditions under which Stoke's formula is applicable. Hence, the reason (R) is also **true**. 5. **Conclusion**: - Both the assertion (A) and the reason (R) are true. However, the reason correctly explains why the assertion is true, establishing a cause-and-effect relationship. ### Final Answer: Both A and R are true, and R is the correct explanation of A. ---
Promotional Banner

Similar Questions

Explore conceptually related problems

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. What is the viscous force on a glass sphere of radius r=1mm falling through water (eta=1xx10^(-3)Pa-s) when the sphere has speed of 3m/s?

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Calculate the highest average speed that blood (rho~~1000kg//m^(3) ) could have and still remain in laminar flow when it flows through the arorta (R=8xx10^(-3)m ) Take the coeffiicient of viscosity of blood to be 4xx10^(-3)Pa-s

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. If the sphere in previous question has mass of 1xx10^(-5)kg what is its terminal velocity when falling through water? (eta=1xx10^(-3)Pa-s) A. 1.3m/s B. 3.4m/s C. 5.2m/s D. 6.5m/s

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Blood vessel is 0.10 m in length and has a radius of 1.5xx10^(-3) m blood flows at rate of 10^(-7)m^(3)//s through this vessel. The pressure difference that must be maintained in this flow between the two ends of the vessel is 20 Pa what is the viscosity sufficient of blood?

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Which of the following may be concluded from the information in the passage?