The dimension \([ML^{-2}T^{-2}A^2]\) belong to the:
[2022]
The dimension of magnetic permeability is \(MLT^{-2}A^{-2}\). The given dimension \(ML^{-2}T^{-2}A^2\) does not match a standard physical quantity listed. Assuming a typo and it refers to magnetic permeability.
If \(E\) and \(G\) respectively denote energy and gravitational constant, then \(\frac{E}{G}\) has the dimensions of:
[2021]
Energy \([E] = ML^2T^{-2}\) and Gravitational Constant \([G] = M^{-1}L^3T^{-2}\). So \([E/G] = M^2L^{-1}T^0\).
Dimensions of stress are:
[2020]
Stress is Force per unit Area. \([\text{Stress}] = [F]/[A] = (MLT^{-2})/L^2 = ML^{-1}T^{-2}\).
The dimensions of \((\mu_0\epsilon_0)^{-1/2}\) are:
[2012 Mains]
The speed of light \(c = 1/\sqrt{\mu_0\epsilon_0}\). Therefore, \((\mu_0\epsilon_0)^{-1/2} = c\). The dimensions of speed are \([LT^{-1}]\).
The dimension of \(\frac{1}{2}\epsilon_0 E^2\), where \(\epsilon_0\) is permittivity of free space and \(E\) is electric field, is:
[2010 Pre]
The expression \(\frac{1}{2}\epsilon_0 E^2\) represents electric energy density, which is Energy per unit Volume. \([\text{Energy density}] = [\text{Energy}]/[\text{Volume}] = (ML^2T^{-2})/L^3 = ML^{-1}T^{-2}\).
Which two of the following five physical parameters have the same dimensions?
A. Energy density
B. Refractive index
C. Dielectric constant
D. Young’s modulus
E. Magnetic field
[2008]
Energy density (A) is \(ML^{-1}T^{-2}\). Young's modulus (D) is Stress/Strain, so also \(ML^{-1}T^{-2}\). Therefore, (A) and (D) have the same dimensions.
Dimensions of resistance in an electrical circuit, in terms of dimension of mass \(M\), of length \(L\), of time \(T\) and of current \(I\), would be:
[2007]
Resistance \(R = V/I = (W/q)/I = W/(I^2T)\). Work \([W] = ML^2T^{-2}\). So, \([R] = (ML^2T^{-2})/(I^2T) = ML^2T^{-3}I^{-2}\).
The dimensions of universal gravitational constant are:
[2004]
From \(F = G \frac{m_1 m_2}{r^2}\), we get \(G = \frac{Fr^2}{m_1 m_2}\). So, \([G] = \frac{(MLT^{-2})(L^2)}{M^2} = M^{-1}L^3T^{-2}\).
The dimensional formula of permeability of free space \(\mu_0\) is
[1991]
From Ampere's law, the dimensions of permeability of free space \(\mu_0\) are derived as \(MLT^{-2}A^{-2}\).
According to Newton, the viscous force acting between liquid layers of area \(A\) and velocity gradient \( \Delta v / \Delta z \) is given by \(F = -\eta A (\Delta v / \Delta z)\), where \(\eta\) is constant called coefficient of viscosity. The dimensional formula of \(\eta\) is:
[1990]
From the formula \(F = -\eta A (\Delta v / \Delta z)\), the dimension of \(\eta\) is \(F / (A \cdot (\Delta v / \Delta z)) = [MLT^{-2}] / ([L^2] \cdot [T^{-1}]) = [ML^{-1}T^{-1}]\).