• # 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.

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