$A$ road is $10\, m$ wide. Its radius of curvature is $50\, m$. The outer edge is raised above the inner edge by a distance of $1.5\, m$. This road is most suited for the velocity .......... $m/s$. (in $.5$)

The $pH$ of $0.05 \ M$ acetic acid is $(K_a = 2 \times 10^{-5})$

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

The plates of a parallel plate capacitor are charged up to $200 \ V$. $A$ dielectric slab of thickness $4 \ mm$ is inserted between its plates. Then,to maintain the same potential difference between the plates of the capacitor,the distance between the plates is increased by $3.2 \ mm$. The dielectric constant of the dielectric slab is:

In agarose gel electrophoresis,$DNA$ molecules are separated on the basis of their