$A$ ball is projected with velocity $V_0$ at an angle of elevation $30^\circ$. Mark the correct statement.

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\,K$. If the temperature of the source is kept constant and its efficiency is raised to $60\%$,then the required temperature of the sink will be .... $K$.

The ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is

Which carbonyl compound has the maximum dipole moment?

Consider a block of conducting material of resistivity ' $\rho$ ' as described. Current ' $I$ ' enters at ' $A$ ' and leaves from ' $D$ '. We apply the superposition principle to find the voltage ' $\Delta V$ ' developed between ' $B$ ' and ' $C$ '. The calculation is done in the following steps:
$(i)$ Take current ' $I$ ' entering from ' $A$ ' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate the field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at ' $r$ '.
(iii) From the ' $r$ ' dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
(iv) Repeat $(i)$,(ii),and (iii) for current ' $I$ ' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '.
For current entering at $A$,the electric field at a distance ' $r$ ' from $A$ is:

$A$ wire in the form of a square of side '$a$' carries a current $i$. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space = $\mu_0$)