A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.2 m/s2. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is _________.
Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side a. The surface tension of the soap film is $$\gamma$$. The system of charges and planar film are in equilibrium, and $$a = k{\left[ {{{{q^2}} \over \gamma }} \right]^{1/N}}$$, where k is a constant. Then N is __________.
The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10$$-$$25 kg. The mass (in mg) of the radioactive sample is _________.
A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 $$\Omega$$ and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as $$I = {I_0}\cos (300t)$$, where I0 is constant. If the magnetic moment of the loop is $$N{\mu _0}{I_0}\sin (300t)$$, then N is ___________.
