Consider the following anions:
$(I)$ $CF_{3}SO_{3}^{-}$
$(II)$ $C_{6}H_{5}SO_{3}^{-}$
$(III)$ $C_{6}H_{5}O^{-}$
$(IV)$ $CH_{3}COO^{-}$
When attached to $sp^{3}$-hybridized carbon,their leaving group ability in nucleophilic substitution reaction decreases in the order:

It is estimated that per minute each $cm^2$ of the Earth receives about $2 \ cal$ $(1 \ cal = 4.18 \ J)$ of heat energy from the Sun. This is called the Solar constant. In $SI$ units,the value is:

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:

On heating a mixture of $SO_2Cl_2$ and $CO$,two equilibria are simultaneously established:
$SO_2Cl_{2(g)} \rightleftharpoons SO_{2(g)} + Cl_{2(g)}$
$CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}$
On adding more $SO_2$ at equilibrium,what will happen?

$A$ string of mass $m$ and length $l$ hangs from the ceiling as shown in the figure. $A$ wave in the string moves upward. $v_A$ and $v_B$ are the speeds of the wave at points $A$ and $B$ respectively. Then $v_B$ is

Gas is being pumped into a spherical balloon at the rate of $30 \ ft^3 / min$. The rate at which the radius increases when it reaches the value $15 \ ft$, is: