KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    Figure shows a metal ball of mass 50 kg and radius \[\frac{2}{\sqrt{\pi }}m\] is placed on an insulating uncharged stand, in space an upward electric field  \[5\times {{10}^{5}}N/C\] is switched on. A stream of light ions is incident on the ball from left side at a speed \[2\times {{10}^{6}}m/s\] shown in figure. If charge on ball at \[t=0\] was zero, find the time in seconds at which ball will be lifted from the stand. The charge density of ion beam is \[5\times {{10}^{-12}}coul/{{m}^{3}}\].  Assume that all charge incident on the ball is absorbed.

    A) 10 sec.

    B) 15 sec.          

    C) 20 sec.         

    D) 25 sec.

    Correct Answer: D

    Solution :

    Ball will lift when \[qE\ge mg\]
    \[(\rho Av)t\,E\,\ge mg\]
    \[t\ge \frac{mg}{\rho AvE}\,\,;\frac{50\times 10}{t\ge 5\times {{10}^{-12}}\times \pi {{\left( \sqrt{\frac{2}{\pi }} \right)}^{2}}\times 2\times {{10}^{6}}\times 5\times {{10}^{5}}\,}\,;\,t\ge 25\,sec.\]

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