Choose the INCORRECT dimensions:
Step 1: The speed of light does not have dimensions of mass or length squared. It is dimensionless with respect to mass and length.
Step 2: Option (C) incorrectly states the dimensions of the speed of light.
Step 3: The correct dimensions of the speed of light should be \( L T^{-1} \).
Hence, (C) is incorrect.
Match List-I with List-II.
Choose the correct answer from the options given below :
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
A quantity \( X \) is given by: \[ X = \frac{\epsilon_0 L \Delta V}{\Delta t} \] where:
- \( \epsilon_0 \) is the permittivity of free space,
- \( L \) is the length,
- \( \Delta V \) is the potential difference,
- \( \Delta t \) is the time interval.
The dimension of \( X \) is the same as that of: