There is a small hole in a hollow sphere. Water enters it when it is taken to a depth of $40 \,cm$ under water. The surface tension of water is $0.07 \,N/m$. The diameter of the hole is .......... $mm$.

Which of the following alcohols reacts most rapidly with alkali metals?

$A$ ball falls from a height $h$ and rebounds after striking the floor. The coefficient of restitution is $e$. The total distance covered before it comes to rest is

The solution of $x \frac{dy}{dx} = y + x e^{y/x}$ with $y(1) = 0$ is

In order to oxidize a mixture of one mole of each of $FeC_2O_4$,$Fe_2(C_2O_4)_3$,$FeSO_4$,and $Fe_2(SO_4)_3$ in an acidic medium,the number of moles of $KMnO_4$ required is:

If two glass plates have water between them and are separated by a very small distance (see figure),it is very difficult to pull them apart. This is because the water in between forms a cylindrical surface on the side that gives rise to a lower pressure in the water in comparison to the atmosphere. If the radius of the cylindrical surface is $R$ and the surface tension of water is $T$,then the pressure in the water between the plates is lower by: