Units & Measurements

The dimension of \(\left( {{1 \over 2}} \right){\varepsilon _0}{E^2}\)
( \({\varepsilon _0}\) : permittivity of free space, E electric field )

The SI unit of inductance, the henry can be written as

Let [\({\mathrm\varepsilon}_\mathrm o\)] denote the dimentional formula of the permittivity of the vacuum, and [\(\mu_o\)] that of the permeability of the vacuum.If M = mass, L = length, T = time and I = electric current,

The equation of state for real gas is given by \(\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT\). The dimention of the constant a is ___________.

The pairs of physical quantities that have the same dimensions is (are):

Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some of the physical quantities may have more than one choice correct:

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In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are _____________

The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)

Plank' constant has dimension __________.

Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and charge (Q) given in column II and write the correct answer against the matched quantity in a tabular form in your answe...

Write the dimensions of the followings in terms of mass, time, length and charge
(i) magnetic flux
(ii) rigidity modulus

A gas bubble, from an explosion under water, oscillates with a period T proportional to padbEc. Where 'P' is the static pressure, 'd' is the density of water and 'E' is the total energy of the explosion. Find the value of a, b and c.

Give the MKS units for each of the following quantities.
(i) Young's modulus
(ii) Magnetic Induction
(iii) Power of a lens