Question

Initial speed of an alpha particle side a tube a length $4m$ is $1km/s$, if it is accelerated in the tube and comes out with a speed of $9km/s$, then the time for which the particle remains inside the tube is

• A. $8\times {10}^{-3}s$
• B. $8\times {10}^{-4}s$
• C. $80\times {10}^{-3}s$
• D. $800\times {10}^{-3}s$

Answer 1

The correct option is B $8\times {10}^{-4}s$

Initial speed, $u=1km/s=1000m/s$
Final speed, $v=9km/s=9000m/s$
By using the relation
$v^2=u^2+2as$
$(9000{)}^2=(1000{)}^2+2\times a\times 4$
$a={10}^{7}m/s^2$
$\therefore$ the time for which the particle remains in the tube
$v=u+at$
or $t=\frac{v-u}{a}=\frac{9000-1000}{{10}^7}$
$=8\times {10}^{-4}s$.