The plates of a parallel plate capacitor are charged up to $100 \, V$. $A$ $2 \, mm$ thick plate is inserted between the plates. To maintain the same potential difference,the distance between the capacitor plates is increased by $1.6 \, mm$. The dielectric constant of the plate is:

We have two spheres,one of which is hollow and the other solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by:

$A$ light wave is travelling along the $y-$ direction. If the corresponding $\vec E$ vector at any time is along the $x-$ axis,the direction of the $\vec B$ vector at that time is along:

Acetic acid is reacted with metallic sodium to form hydrogen and $X$. When $X$ is heated with sodalime,$Y$ and sodium carbonate are formed. $Y$ is

In the circuit shown, if a conducting wire is connected between points $A$ and $B$, the current in this wire will

The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$) inclined plane is $F_1$,while the minimum force needed to prevent it from sliding down is $F_2$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta = 2 \mu$,then the ratio $\frac{F_1}{F_2}$ is: