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A long horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20A, is in equilibrium at a height of 0.01 m over another parallel long wire CD which is fixed in a horizontal plane and carries a steady current of 30 A, as shown in figure. Show that when AB is slightly depressed, it executes simple harmonic motion. Find the period of oscillations.

Chemistry

At 380^oC, the half-life period for the first order decomposition of H₂O₂ is 360 min. The energy of activation of the reaction is 200 kJ mol ^-1. Calculate the time required for 75% decomposition at 450^oC.

Mathematics

There are n urns, each of these contain n + 1 balls. The ith urn contains i white balls and (n + 1 - i) red balls. Let u_i be the event of selecting ith urn, i = 1, 2, 3............., n and w the event of getting a white ball.

Let