The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\,mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere):-

Observe the following reaction: $2 A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

If $EAN$ of central metal cation $M^{2+}$ in a non-chelating complex is $36$ and atomic number of metal $M$ is $26$,then the number of monodentate ligands in this complex is:

$A$ homogeneous solid cylinder of length $L$ $(L < H/2)$ and cross-sectional area $A'$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid (density $2d$) and $3L/4$ in the lighter liquid (density $d$) as shown in the figure. The density $D$ of the solid is given by:

The $pK_a$ of a weak acid is $4.8$. What should be the ratio of $\frac{[\text{acid}]}{[\text{salt}]}$,if a buffer of $pH=5.8$ is required?

Which one of the following graphs represents the Freundlich adsorption isotherm?