Home
Class 12
PHYSICS
Check the accuracy of the relation T=sqr...

Check the accuracy of the relation `T=sqrt((L)/(g))` for a simple pendulum using dimensional analysis.

Text Solution

Verified by Experts

The dimensions of LHS =the dimension of `T=|M^(0)L^(0)T^(1)|`
The dimensions of RHS `=(("dimensions of length")/("dimensions of acceleration"))^(1//2)` (`therefore 2pi` is a dimensionless constant)
`[(L)/(LT^(2))]^(1//2)=[T^(2)]^(1//2)=[T]=[M^(0)L^(0)T^(1)]`
Since the dimensions are same on both the sides, the relation is correct.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Check the accuracy of the relation T=2pisqrt((L)/(g)) for a simple pendulum using dimensional analysis.

Uses of Dimensional analysis

Use and Limitation OF Dimensional Analysis

Check the accuracy of the relation v=(1)/(2l)sqert((T)/(m)) ,where v is the frequency, l is legth, T is tension and m is mass per unit legth of the string.

Deduce the relation for the time period of a simple pendulum.

The graph of l against T for a simple pendulum is

Check the accuracy of the relation s = ut + (1)/(2)at^(2) where s is the distance travelled by the with uniform acceleration a in time t and having initial velocity u.

It is known that the time of revolution T of a satelite around the earth depends on the universal gravitational constant G, the mass of the earth M, and the radius of the circular orbit R. Obtain an expression for T using dimensional analysis.

Write a short note on applications and uses of dimensional analysis.

ALLEN-BASIC MATHS-UNIT & DIMENSIONS
  1. Find the SI unit of (i) area, (ii) density, and (iii) momentum.

    Text Solution

    |

  2. Write dimensional formula of mass and speed.

    Text Solution

    |

  3. Convert 1 newton (SI unit of force) into dyne (CGS unit of force)

    Text Solution

    |

  4. The acceleration due to gravity is 9.8 m s^(-2). Give its value in ft ...

    Text Solution

    |

  5. Check the accuracy of the relation T=sqrt((L)/(g)) for a simple pendul...

    Text Solution

    |

  6. It is known that the time of revolution T of a satellite around the ea...

    Text Solution

    |

  7. Find dimensional formula :

    Text Solution

    |

  8. If alpha=F/v^(2) sin beta t, find dimensions of alpha and beta. Here v...

    Text Solution

    |

  9. In system called the star system we have 1 star kilogram =10^(20) kg. ...

    Text Solution

    |

  10. The position of a particle at time t is given by the relation x(t)=(v(...

    Text Solution

    |

  11. If the velocity (V) , acceleration (A) , and force (F) are taken as fu...

    Text Solution

    |

  12. Number of particles is given by n=-D(n(2)-n(1))/(x(2)-x(1)) crossing a...

    Text Solution

    |

  13. The dimensions of 1/2 epsilon(0)E^(2) (epsilon(0)= permittivity of fre...

    Text Solution

    |

  14. Force F and density D are related as F=(alpha)/(beta+sqrtd), Then find...

    Text Solution

    |

  15. If discharge rate is given by V=(pi Pr^(4))/(8 mu l) then find out the...

    Text Solution

    |

  16. In an imeganary experiment, the Yound's modulus Y of a material is giv...

    Text Solution

    |

  17. Find the dimension of the quantity (1)/(4pi epsilon(0))(e^(2))/(hc), t...

    Text Solution

    |

  18. Are there any physical quantities out of the following which have the ...

    Text Solution

    |

  19. Find the dimensions of a in the formula (p+a/V^2)(V-b)=RT

    Text Solution

    |