NEET Unit And Dimensions MCQs & PYQs

From \(F = G \frac{m_1 m_2}{r^2}\), we get \(G = \frac{Fr^2}{m_1 m_2}\). So, \([G] = \frac{(MLT^{-2})(L^2)}{M^2} = M^{-1}L^3T^{-2}\).

A dimensional constant is a physical constant with dimensions. The Gravitational constant \(G\) is a dimensional constant with dimensions \(M^{-1}L^3T^{-2}\).

The product \(RC\) represents the time constant of an \(RC\) circuit, and its dimension is time, \(T\).

Pressure is defined as Force per unit Area. Its dimensions are \(MLT^{-2} / L^2 = ML^{-1}T^{-2}\).

From Ampere's law, the dimensions of permeability of free space \(\mu_0\) are derived as \(MLT^{-2}A^{-2}\).

From the formula \(F = -\eta A (\Delta v / \Delta z)\), the dimension of \(\eta\) is \(F / (A \cdot (\Delta v / \Delta z)) = [MLT^{-2}] / ([L^2] \cdot [T^{-1}]) = [ML^{-1}T^{-1}]\).

Energy per unit volume, force per unit area, and product of voltage and charge per unit volume all have dimensions \(ML^{-1}T^{-2}\). Angular momentum has dimensions \(ML^2T^{-1}\), which is different.

The energy stored in an inductor is \(U = \frac{1}{2}LI^2\). Therefore, the dimensions of self-inductance \(L\) are \(U/I^2 = [ML^2T^{-2}]/[A^2] = [ML^2T^{-2}A^{-2}]\).

Torque is calculated as Force \(\times\) perpendicular distance. So its dimensions are \([MLT^{-2}] \times [L] = [ML^2T^{-2}]\).

The product \(CR\) is the time constant of an RC circuit. Its dimension is time, \(T\), which can be written as \(M^0L^0T^1\).