Inside a vessel filled with liquid a converging lens is placed as shown in figure. The lens has focal length $$15 \mathrm{~cm}$$ when in air and has refractive index $$\frac{3}{2}$$. If the liquid has refractive index $$\frac{9}{5}$$, the focal length of lens in liquid is

A metal wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $$=25 \sqrt{2} \Omega, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ and Earth's horizontal component of magnetic field $$\left.\mathrm{B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}\right)$$

A body is projected from earth's surface with thrice the escape velocity from the surface of the earth. What will be its velocity when it will escape the gravitational pull?

The depth at which acceleration due to gravity becomes $$\frac{\mathrm{g}}{\mathrm{n}}$$ is [ $$\mathrm{R}$$ = radius of earth, $$\mathrm{g}=$$ acceleration due to gravity, $$\mathrm{n}=$$ integer $$]$$