An electron moves through a uniform magnetic field $$\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T$$. At a particular instant of time, the velocity of electron is $$\vec{u}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$$. If the magnetic force acting on electron is $$\vec{F}=5 e \hat{k} N$$, where $$e$$ is the charge of electron, then the value of $$B_0$$ is _________ $$T$$.

A parallel plate capacitor with plate separation $$5 \mathrm{~mm}$$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $$2 \mathrm{~mm}$$, while keeping the battery connections intact, the capacitor draws $$25 \%$$ more charge from the battery than before. The dielectric constant of the sheet is _________.

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02 \%$$ is _______ $$m$$.

(Take density of sea water $$=10^3 \mathrm{kgm}^{-3}$$, Bulk modulus of rubber $$=9 \times 10^8 \mathrm{~Nm}^{-2}$$, and $$g=10 \mathrm{~ms}^{-2}$$)

A body starts falling freely from height $$H$$ hits an inclined plane in its path at height $$h$$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $$\frac{H}{h}$$ for which the body will take the maximum time to reach the ground is __________.