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

The density of gold is 19.3 gm/cc. Express its value in the SI unit.

The density of gold is 19.3 gm/cc. Express its value in the SI unit.

Share My Answer
1

1 Answer

Solution:

Since gm/cc and Kg/m3 are CGS and SI units of density respectively. The dimensional formula of density is d = [ML-3T0] and comparing it with [MxLyTz] we get,

x = 1, y = -3 and z = 0

CGS System

n1 = 19.3 g/cc

M1 = 1 gm

L1 = 1 cm

T1 = 1 sec.

SI System

n2 = ?

M2 = 1 kg

L2 = 1 m

T2 = 1 sec

We have, the unit conversion formula using the dimensional method is

\(n_2=n_1\left[\frac{M_1}{M_2}\right]^x\left[\frac{L_1}{L_2}\right]^y\left[\frac{T_1}{T_2}\right]^z\)

\(=19.3\left[\frac{1gm}{1kg}\right]^1\left[\frac{1cm}{1m}\right]^{-3}\left[\frac{1sec}{1sec}\right]^0\)

\(=19.3\left[\frac{1gm}{1000gm}\right]^1\left[\frac{1cm}{100cm}\right]^{-3}1\)

\(=19.3\times10^{-3}\times10^6\times1\)

= 19300

i.e. 19.3 gm/cc = 19300 kg/m3

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