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A particle P is sliding down a frictionless hemispherical bowl. It passes the point Aat t equals 0. At this instant of time, the horizontal component of its velocity v. A bead Q of the same mass as P is ejected from A to t equals 0 along the horizontal string A B (see figure) with the speed v. Friction between the bead and the string may be neglected. Let t subscript p end subscript and t subscript Q end subscript be the respective time taken by P and Q to reach the point B. Then

  1. t subscript p end subscript less than t subscript Q end subscript    
  2. t subscript p end subscript equals t subscript Q end subscript    
  3. t subscript p end subscript greater than t subscript Q end subscript    
  4. All of these    

The correct answer is: t subscript p end subscript less than t subscript Q end subscript


    For particle P, motion between A and C will be an accelerated one while between C and B a retarded one. But in any case horizontal component of it’s velocity will be greater than or equal to v on the other hand in case of particle Q, it is always equal to v. Horizontal displacement of both the particles are equal, so t subscript P end subscript less than t subscript Q end subscript

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