UI
Toolbox
  • Dictionary
    Dictionary
  • Calculator
    Calculator
Grade -11 (NEB) > Science Physics Dimensional Analysis and Applications, Physical Quantities

Check the correctness of the given equation, v = u + 5 at

Check the correctness of the given equation by using dimensional analysis. v = u + 5 at,

Share My Answer
1

1 Answer

Solution:

Here, the given expression is

v = u + 5 at

The dimension of LHS

= \(\left[LT^1\right]\)

The dimension of RHS

= \(\left[LT^1\right]+5\left[LT^{-2}\right]\left[T\right]\)

= \(\left[LT^1\right]+5\left[LT^{-1}\right]\)

= \(6\left[LT^{-1}\right]\)

Here, 6 is a dimensionless quantity. So, dimension of LHS = dimension of RHS. Thus, the given equation is dimensionally correct.

1

Comments

Things to Remember From Physical Quantities

  • The four applications of dimensional analysis are:
    • To check the correctness of physical relation.
    • To derive the relation between various physical quantities.
    • To convert the value of physical quantities from one system of units into another system of units.
    • To find the dimensions of constants in the given equation.

  • The correctness of physical relation can be determined by comparing the dimension of the left-hand side (LHS) and the dimension of the right-hand side (RHS)
  • We can use the formula, \(N_2=N_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c\)\) to convert unit from one to another system using dimension.

  • Despite the usefulness of dimensions, there are some limitations. They are:
    • The dimensional analysis does not give any information about dimensionless constants.
    • If the quantity depends on more than three other physical quantities having dimensions, the formula cannot be derived.
    • We cannot derive the formula containing trigonometric functions, logarithmic functions, exponential functions, etc. It is best suited for linear functions only.
    • The exact form of a relationship cannot be determined when there is more than one part in any relationship.
    • It gives no information about the physical quantity,

 

Topics from Physics

Physical Quantities 27 Electricity & Magnetism 48 Motion 8 Measurement 4 Electricity 166 Physical Optics 80 Waves 117 Force 51 Heat 137 Laws of Motion 1 Light 100 Pressure 139 Thermodynamics 1

Related Questions