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IIT JEE 2006 Paper : PHYSICS Section IV - Subjective Problems

This section contains 4 numerical problems. The answer to each of the questions would lie between 0 and 9999. You have to simply write the correct numerical value in the input box provided. You will be awarded 6 marks for correct numerical value and 0 for an incorrect value.
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iit_jee_2006_physics_subjective_problems_1a.jpg A uniform rectangular plate ABCD of length a, width b and mass M is free to rotate about its hinged edge AB. The plate is held in a horizontal position by a stream of small particles each of mass m hitting the shaded half of the plate perpendicularly. The stream contains n particles per m 2 per second and each particle collides elastically with the plate. What is the velocity v of the particles in ms −1 so that the plate remains in the horizontal position?
AB = a = 2 m, BC = b = 1 m, M = 3 kg, m = 0.01 kg, n = 100 and acceleration due to gravity g = 10 ms −2.

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