A coil 10 turns and a resistance of $$40 \Omega$$ is connected in series with B.G. of resistance $$30 \Omega$$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $$10^{-2} \mathrm{~T}$$. If it is now turned through an angle of $$60^{\circ}$$ about on axis in its plane. Find the charge indicted in the coil. (Area of a coil $$=10^{-2} \mathrm{~m}^2$$ )

A geostationary satellite revolves around the Earth in a circular orbit of radius $$4 R$$. Here, $R$ is the radius of the Earth. Then, the time period of another satellite moving in a circular orbit of radius $$2 R$$ is:

Two long parallel wires carry equal current $$i$$ flowing in the same directions are at a distance $$4 d$$ apart. The magnetic field $$B$$ at a point $$P$$ lying on the perpendicular line joining the wires and at a distance $$x$$ from the mid-point is

0.5 mole of an ideal gas at constant temperature $$27^{\circ} \mathrm{C}$$ kept inside a cylinder of length $$L$$ and cross-section $$A$$ closed by a massless piston. The cylinder is attached with a conducting rod of length L$$_1$$ cross-section area $$(1 / 9) \mathrm{m}^2$$ and thermal conductivity $$k_1$$ whose other end is maintained at $$0^{\circ} \mathrm{C}$$. If piston is moved such that rate of heat flow through the conduction rod is constant then velocity of piston when it is at height $$L / 2$$ from the bottom of cylinder is (neglect any kind of heat loss from system)