The densities of two solid spheres A and B of the same radii R vary with radial distance r as $${\rho _A}(r) = k\left( {{r \over R}} \right)$$ and $${\rho _B}(r) = k{\left( {{r \over R}} \right)^5}$$, , respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are $${I_A}$$ and $${I_B}$$, respectively. If, $${{{I_B}} \over {{I_A}}} = {n \over {10}}$$, the value of n is

The energy of a system as a function of time t is given as E(t) = $${A^2}\exp \left( { - \alpha t} \right)$$, where $$\alpha = 0.2\,{s^{ - 1}}$$. The measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 %, the percentage error in the value of E(t) at t = 5 s is

In terms of potential difference V, electric current I, permittivity $${\varepsilon _0}$$, permeability $${\mu _0}$$ and speed of light c, the dimensionally correct equation(s) is(are) :

Four harmonic waves of equal frequencies and equal intensities I₀ have phase angles 0, $${\pi \over 3},{{2\pi } \over 3}$$ and $$\pi$$. When they are superposed, the intensity of the resulting wave is nI₀. The value of n is