A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s², find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m$$^2$$. The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio $$n_B/n_A$$, where $$n_A$$ and $$n_B$$ are the number of moles of air in bubbles A and B, respectively. (Neglect the effect of gravity.)

A steady current I goes through a wire loop PQR having shape of a right angle triangle wit6h PQ = 3, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is $$k\left( {{{{\mu _0}I} \over {48\pi x}}} \right)$$, find the value of $$k$$.

A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice. (Take atmospheric pressure = 1.0 $$\times$$ 10$$^5$$ N/m$$^2$$, density of water = 1000 kg/m$$^3$$ and g = 10 m/s$$^2$$. Neglect any effect of surface tension.)