A body is released from the top of a tower '$$\mathrm{H}$$' metre high. It takes $$t$$ second to reach the ground. The height of the body $$\frac{t}{2}$$ second after release is

There is a second's pendulum on the surface of earth. It is taken to the surface of planet whose mass and radius are twice that of earth. The period of oscillation of second's pendulum on the planet will be

Two long parallel wires carrying currents $$8 \mathrm{~A}$$ and $$15 \mathrm{~A}$$ in opposite directions are placed at a distance of $$7 \mathrm{~cm}$$ from each other. A point '$$\mathrm{P}$$' is at equidistant from both the wires such that the lines joining the point to the wires are perpendicular to each other. The magnitude of magnetic field at point '$$\mathrm{P}$$' is $$(\sqrt{2}=1.4) ( \mu_0=4 \pi \times 10^{-7}$$ SI units)

A body of mass 200 gram is tied to a spring of spring constant $$12.5 \mathrm{~N} / \mathrm{m}$$, while other end of spring is fixed at point '$$O$$'. If the body moves about '$$O$$' in a circular path on a smooth horizontal surface with constant angular speed $$5 \mathrm{~rad} / \mathrm{s}$$ then the ratio of extension in the spring to its natural length will be