Home
Class 11
PHYSICS
The force F on a sphere of radius r movi...

The force F on a sphere of radius r moving in a medium with velocity v is given by `F = 6 pi eta rv`. The dimensions of `eta` are

A

`[ML^(-3)]`

B

`[MLT^(-2)]`

C

`[MT^(-1)]`

D

`[ML^(-1T^(-1))]`

Text Solution

Verified by Experts

The correct Answer is:
D

`[eta] = [(F)/(av)] = [MLT^(-2)/(LLt^(-1)]]`
Promotional Banner

Topper's Solved these Questions

  • UNIT AND DIMENSIONS

    DC PANDEY ENGLISH|Exercise More Than One Correct|5 Videos
  • UNIT AND DIMENSIONS

    DC PANDEY ENGLISH|Exercise Subjective|16 Videos
  • UNIT AND DIMENSIONS

    DC PANDEY ENGLISH|Exercise Assertion And Reason|2 Videos
  • THERMOMETRY,THERMAL EXPANSION & KINETIC THEORY OF GASES

    DC PANDEY ENGLISH|Exercise Level 2 Subjective|9 Videos
  • UNITS, DIMENSIONS & ERROR ANALYSIS

    DC PANDEY ENGLISH|Exercise Medical entrances gallery|32 Videos

Similar Questions

Explore conceptually related problems

A force F is given by F = at+ bt^(2) , where t is time. The dimensions of a and b are

The viscous drug on a sphere of medis, moving through a fluid with velocity can be expressed as 6 pi eta where eta is the coefficient of viscosity of the fluid. A small sphere of radius a and density sigma is released from the bottom of a column of liqaid of density rho . If rho ger than sigma describe the motion of the sphere. Deduce an expression for (i) initial acceleration of the sphere and (ii) its terminal velocity

If force F is applied on a body and it moves with a velocity v, the power will be

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. 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

A force F is given by F = at + bt^(2) , where t is time . What are the dimensions of a and b ?

A force F is given by F = at + bt^(2) , where t is time . What are the dimensions of a and b ?

A container filled with viscous liquid is moving vertically downwards with constant speed 3v_0 . At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed v_0 . The coefficient of viscosity is eta . There is no relative motion between the liquid and the container. Then at the shoen instant, The magnitude of viscous force acting on sphere is

In the block moves up with constant velocity v m/s. Find F

(A) : Relative to an observer at rest in a medium the speed of a mechanical wave in that medium (1) depends only on elastic and other properties (such as mass density) of the medium. It does not depend on the velocity of the source. (B): For an observer moving with velocity v_(0) relative to the medium, the speed of a wave is obviously different from v and is given by v+-v_(0)

DC PANDEY ENGLISH-UNIT AND DIMENSIONS-Single Correct
  1. the dimensional formula for planck's constant and angular momentum ar...

    Text Solution

    |

  2. Dimension of velocity gradient is

    Text Solution

    |

  3. Which of the following is the dimension of the coefficient of frintion...

    Text Solution

    |

  4. Which of the following sets have different dimensions ?

    Text Solution

    |

  5. The force F on a sphere of radius r moving in a medium with velocity v...

    Text Solution

    |

  6. A force F is given by F = at + bt^(2) , where t is time . What are the...

    Text Solution

    |

  7. The physical quanitity the dimensions [M^(1)L^(2)T^(-3)A^(-1)] is

    Text Solution

    |

  8. The dimensional formula for planck's magnetic flux is

    Text Solution

    |

  9. Choose the wrong statement. Option 1 All quantities may be represen...

    Text Solution

    |

  10. If unit of length and time is double, dthe numerical valuure of 'g' (a...

    Text Solution

    |

  11. Using mass (M), "length"(L) , time (T) and current (A) as fundamental...

    Text Solution

    |

  12. The equation of a wave is given by y = a sin omega [(x)/v -k] w...

    Text Solution

    |

  13. If the energy ( E) ,velocity (v) and force (F) be taken as fundamental...

    Text Solution

    |

  14. If "force" F, "length" L and time T are taken as fundemental unit , t...

    Text Solution

    |

  15. The ratio of the dimensions of plank's constant and that of the moment...

    Text Solution

    |

  16. Given that y = A sin [((2 pi )/(lambda)(ct - x))] where y and x are me...

    Text Solution

    |

  17. Which of the following sets cannot enter into the list of fundamental ...

    Text Solution

    |

  18. In the formula X = 3Y Z^(2) , X and Z have dimensions of capacitance...

    Text Solution

    |

  19. A quantity X is given by epsilon(p) L(delta V)/(delta t) , where eps...

    Text Solution

    |

  20. In the relaction p = (a)/(beta) e ^((aZ)/(k theta ), p is pressure Z ...

    Text Solution

    |