Units and Measurements

Identify the pair whose dimensions are equal

Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are

The physical quantities not having same dimensions are

Which one of the following represents the correct dimensions of the coefficient of viscosity?

Out of the following pair, which one does NOT have identical dimensions is

The dimension of magnetic field in M, L, T and C (coulomb) is given as

Let [$${\varepsilon _0}$$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:

Expression for time in terms of G(universal gravitional constant), h (Planck constant) and c (speed of light) is proportional to :

In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :

Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length ?

If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:

Which of the following combinations has the dimension of electrical resistance ($$\in$$_0 is the permittivity of vacuum and $$\mu$$₀ is the permeability of vacuum)?

In the formula X = 5YZ² , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :-

In SI units, the dimensions of $$\sqrt {{{{ \in _0}} \over {{\mu _0}}}}$$ is :

Let $$\ell$$, r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of $${\ell \over {rCV}}$$ in SI units will be :

The force of interaction between two atoms is given by F = $$\alpha$$$$\beta$$exp $$\left( { - {{{x^2}} \over {\alpha kt}}} \right)$$; where x is the distance, k is the Boltzmann constant and T is temperature and $$\alpha$$ and $$\beta$$ are two constants. The dimension of $$\beta$$ is :

The dimension of stopping potential V₀ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :