If $E$ and $E_0$ denote energies at time $t$ and $t_0$ respectively, and $L$ and $L_0$ distance from same point at $t$ and $t_0$ respectively, then which of the following equations can be declared to be incorrect on dimensional grounds? (A) $E=\frac{2 E_0 L}{L_0}$ (B) $E=E_0 e^{-2 L / L_0}$ (C) $E=2 L e^{-L / E_0}$ (D) $E=2\left(E_0 / L_0\right) \times e^{-L / L_0}$

In an experiment the angles are required to be measured using an instrument in which 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half a degree $\left(=0.5^{\circ}\right)$, then the least count of the instrument is

The dimension of $\frac{E^2}{\mu_0}$ in mass $(M)$, length $(L)$ and time

$(T)$ is $(E=$ electric field,

$\mu_0=$ permeability of free space)

The surface tension of 70 dynes $/ \mathrm{cm}$ is equal to