Home
Class 11
PHYSICS
Assuming that the mass m of the largest ...

Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity `upsilon,` of water, its density `rho` and acceleration due to gravity g, then m is directly proportional to

A

`v^(3)`

B

`v^(4)`

C

`v^(5)`

D

`v^(6)`

Text Solution

Verified by Experts

The correct Answer is:
D
`m" "alpha" "v^(a)rho^(b)g^(c)`. Writing the dimensions on both sides
`["M"]=["LT"^(-1)]^(a)["ML"^(-3)]^(b)["LT"^(-2)]^(c)`
`["M"]=["M"^(b)"L"^(a-3b+c)"T"^(-a-2c)]`
`therefore" "b=1`
`a-3b+c=0Rightarrow-a-2c=0`
Solving these, we get
`" "a=6`
Hence, `" "m" "alpha" "v^(6)`
Promotional Banner

Topper's Solved these Questions

  • UNITS, DIMENSIONS & ERROR ANALYSIS

    DC PANDEY ENGLISH|Exercise Check Point 1.2|10 Videos

  • UNITS, DIMENSIONS & ERROR ANALYSIS

    DC PANDEY ENGLISH|Exercise Check Point 1.3|10 Videos

  • UNITS, DIMENSIONS & ERROR ANALYSIS

    DC PANDEY ENGLISH|Exercise Medical entrances gallery|32 Videos

  • UNIT AND DIMENSIONS

    DC PANDEY ENGLISH|Exercise Assertion And Reason|2 Videos

  • VECTORS

    DC PANDEY ENGLISH|Exercise Medical enrances gallery|9 Videos

Similar Questions

Explore conceptually related problems

Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity v of the water , its density rho , and the acceleration due to gravity g . Then m is directly proportinal to

It is given that the mass m of the largest stone that can be moved by the folowing river depends upon the velocity v, density rho and acceleration due gravity g. Using dimensions show that m=(kv^(6)rho)/(g^(3)) .

Assume that the largest stone of mass 'm' that can be moved by a flowing river depends upon the velocity of flow v, the density d & the acceleration due to gravity g. I 'm' varies as the K^(th) power of the velocity of flow, then find the value of K.

Experiments reveal that the velocity v of water waves may depend on their wavelength lambda , density of water rho , and acceleration due to gravity g . Establish a possible relation between v and lambda , g, rho .

The velocity of water wave v may depend on their wavelength lambda , the density of water rho and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as

The buoyant force F acting on a body depends on the density of medium rho , volume of body immerese V and acceleration due to gravity g . Establish the relation using method of dimensions.

Derive an expression for the time period (T) of a simple pendulum which may depend upon the mass (m) of the bob, length (l) of the pendulum and acceleration due to gravity (g).

Assuming the mass of Earth to be ten times the mass of Mars, its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth is 10 m//s^(2) . Then the accelration due to gravity on the surface of Mars is given by

Assuming the earth to be a homogeneous sphere of radius R , its density in terms of G (constant of gravitation) and g (acceleration due to gravity on the surface of the earth)

The period P of a simple pendulum is the time for one complete swing. How does P depend on the mass m of the bob, the length l of the string, and the acceleration due to gravity g?

DC PANDEY ENGLISH-UNITS, DIMENSIONS & ERROR ANALYSIS -Check Point 1.1
  1. Give the dimensional formula of (i) gravitational constnat (ii) coeffi...

    Text Solution

    |

  2. If C and R denote capacitance and resistance respectively, then the di...

    Text Solution

    |

  3. Which one of the following have same dimensions :

    Text Solution

    |

  4. Which of the following is a dimensional constant?

    Text Solution

    |

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

    Text Solution

    |

  6. Density of a liquid in CGS system is 0.625g//cm^(3). What is its magni...

    Text Solution

    |

  7. Joule x second is the unit of

    Text Solution

    |

  8. [ML^(2)T^(-3)A^(-1)] is the dimensional formula for

    Text Solution

    |

  9. The dimensional formula fo resistivity in terms of M,L,T and Q where ...

    Text Solution

    |

  10. the dimensional formula for planck's constant and angular momentum ar...

    Text Solution

    |

  11. Which of the following pairs have the same dimensions?

    Text Solution

    |

  12. Which one of the following is not the dimensionless quantity?

    Text Solution

    |

  13. Given that y = a cos((t)/(P) - qx), where t represents distance is met...

    Text Solution

    |

  14. The dimensions of a/b in the equation P=(a-t^(2))/(bx) where P is pre...

    Text Solution

    |

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

    Text Solution

    |

  16. If 'muscle times speed equals power', then what is the ratio of the SI...

    Text Solution

    |

  17. The dimensions of 1/2 in(0) E^(2) (in(0): permittivity of free space, ...

    Text Solution

    |

  18. If P represents radiation pressure , C represents the speed of light ...

    Text Solution

    |

  19. The units of length, velocity and force are doubled. Which of the foll...

    Text Solution

    |

  20. Assuming that the mass m of the largest stone that can be moved by a f...

    Text Solution

    |