Question

A block of mass m and charge q is placed on a smooth horizontal table which terminates in a vertical wall at a distance d from the block. A horizontal electric field E towards right is switched on. Assuming elastic collision, find time period of the resulting oscillatory motion.

• A. $\sqrt{\frac{8dm}{qE}}$
• B. $\sqrt{\frac{4dm}{qE}}$
• C. $\sqrt{\frac{2dm}{qE}}$
• D. none of these

Answer 1

The correct option is A $\sqrt{\frac{8dm}{qE}}$

The equation of motion of block of mass m,
$ma=qE$
$a=\frac{qE}{m}$ and $d=\frac{1}{2}a{t}^2$ (using formula $s=ut+1/2a{t}^2$)
or $t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2dm}{qE}}$
Time period $T=2t=2\sqrt{\frac{2dm}{qE}}$
$=\sqrt{\frac{8dm}{qE}}$