Dimensions of the quantity $\frac{p}{\varepsilon_0 \mu_0}$, where $p$ is the pressure, $\varepsilon_0$ is the electric permittivity of free space, and $\mu_0$ is the permeability of free space, will be:

  • A
    $[MLT^{-4}]$
  • B
    $[MLT^{-2}]$
  • C
    $[ML^{-1}T^0]$
  • D
    $[ML^2T^{-2}]$

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State whether the following statements are true or false:
$(a)$ Weight is a fundamental physical quantity.
$(b)$ $A$ micrometer is used to measure the size of an oleic acid molecule at the molecular level.
$(c)$ The dimensions of a derived quantity obtained from any fundamental quantity can never be zero.

The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

Fill in the blanks:
$(a)$ $1 \ \text{Joule} = \dots \ \text{erg}$
$(b)$ $1 \ \text{eV} = \dots \ \text{Joule}$
$(c)$ $1 \ \text{kWh} = \dots \ \text{Joule}$

Which of the following pairs have the same dimensions?

Which of the following represents the fundamental forces of nature?

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