A galvanometer of resistance 100 $$\Omega $$ has 50 divisions on its scale and has sensitivitv of 20 $$\mu $$A/division. It is to be converted to a voltmeter with three ranges of 0-2V, 0-10 V and 0-20 V. The appropriate circuit to do so is

A point dipole $$\overrightarrow p = - {p_0}\widehat x$$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V= 0 at infinity)

Which of the following combinations has the dimension of electrical resistance ($$ \in $$₀ is the permittivity of vacuum and $$\mu $$₀ is the permeability of vacuum)?

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $$\theta $$₀. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $$\ell $$($$\ell $$ << L), is close to;