A student is provided with a variable voltage source $$\mathrm{V}$$, a test resistor $$R_{T}=10 ~\Omega$$, two identical galvanometers $$G_{1}$$ and $$G_{2}$$ and two additional resistors, $$R_{1}=10 ~M \Omega$$ and $$R_{2}=0.001 ~\Omega$$. For conducting an experiment to verify ohm's law, the most suitable circuit is:

A small particle of mass $$m$$ moves in such a way that its potential energy $$U=\frac{1}{2} m ~\omega^{2} r^{2}$$ where $$\omega$$ is constant and $$r$$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $$n^{\text {th }}$$ orbit will be proportional to,

A child of mass $$5 \mathrm{~kg}$$ is going round a merry-go-round that makes 1 rotation in $$3.14 \mathrm{~s}$$. The radius of the merry-go-round is $$2 \mathrm{~m}$$. The centrifugal force on the child will be

The weight of a body on the surface of the earth is $$100 \mathrm{~N}$$. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is: