Match the Columns: Dimensional Formulas – Rankers Physics

Dimensions: Practice Problem & Solution

Match the column:\n(a) Pressure -> (i) \([ML^2T^{-1}]\)\n(b) Angular Momentum -> (ii) \([M^{-1}L^{-3}T^4A^2]\)\n(c) Magnetic Field -> (iii) \([MT^{-2}A^{-1}]\)\n(d) Permittivity of free space -> (iv) \([ML^{-1}T^{-2}]\)\n(v) \([MT^{-2}A^{-1}]\)
\(a \rightarrow (iv), b \rightarrow (i), c \rightarrow (iv), d \rightarrow (iii)\)
\(a \rightarrow (v), b \rightarrow (ii), c \rightarrow (v), d \rightarrow (iv)\)
\(a \rightarrow (iv), b \rightarrow (i), c \rightarrow (v), d \rightarrow (ii)\)
\(a \rightarrow (i), b \rightarrow (ii), c \rightarrow (iv), d \rightarrow (iii)\)

Solution Explained:

To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:

Pressure = \(F/A = [ML^{-1}T^{-2}]\); Angular Momentum = \(mvr = [ML^2T^{-1}]\); Magnetic field = \(F/qv = [MT^{-2}A^{-1}]\); Permittivity = \([M^{-1}L^{-3}T^4A^2]\).

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

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]
2. A certain body weighs 22.42 g and has a measured volume of 4.7 cc. The possible, error in the measurement of mass and volume are 0.01 g and 0.1 cc. Then maximum error in the density will be: [1991]
3. The dimensions of impulse are equal to that of: [1996]
4. A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading: \(0 \text{mm}\) Circular scale reading: \(52 \text{divisions}\) Given that \(1 \text{mm}\) on main scale corresponds to \(100 \text{divisions}\) on the circular scale. The diameter of the wire from the above data is: [NEET 2020]
5. If dimension of critical velocity of liquid flowing through a tube are expressed as \(v_c \propto \eta^x \rho^y r^z\) where \(\eta\) and \(\rho\) are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of \(x, y\) and \(z\) are given by: [2015-Re]