| 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 \[2\times {{10}^{6}}m/s\] m/s as 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 \[5\times {{10}^{-12}}\text{coul}/{{m}^{3}}.\] 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 \[qE\ge mg\] |
| \[(\rho Av)\,t\,E\ge mg\] |
| \[t\ge \frac{mg}{\rho AvE}\] |
| \[t\ge \frac{50\times 10}{5\times {{10}^{-12}}\times \pi {{\left( \sqrt{\frac{2}{\pi }} \right)}^{2}}\times 2\times {{10}^{6}}\times 5\times {{10}^{5}}}\] |
| \[t\ge 25\sec .\] |
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