If M represents the magnetic dipole moment, B represents the magnetic field, and I represents the moment of inertia, then which of the following physical quantities has the same dimensions as that of MB I ?

Step-by-step solution

The dimensional formula for magnetic dipole moment is [M] = [ A L ^2] . The dimensional formula for magnetic field is [B] = [ M T ⁻² A ⁻¹] . The dimensional formula for moment of inertia is [I] = [ M L ^2] . Now, substituting these into the given expression: [ MB I ] = [ A L ^2][ M T ⁻² A ⁻¹] [ M L ^2] [ MB I ] = [ M L ^2 T ⁻²] [ M L ^2] = [ T ⁻²] Taking the square root: [ MB I ] = [ T ⁻¹] Checking the options, the dimensional formula for velocity gradient ( dv dx ) is [ L T ⁻¹] [ L ] = [ T ⁻¹] , which matches the