QJEEM21Ph5df3: JEE Main 2021 Physics - Class 12 JEEM21Ph5df3 Solution: A body having specific charge 8 C/g is resting on a…

Given,

q = 8 $\mu$ C/g = 8 $\times$ 10 ^{$-$ 6} C/g = 8 $\times$ 10 ^{$-$ 3} C/kg

s = 10 cm = 0.1 m $\Rightarrow$ E = 100 V/m

We know that, acceleration, a = ${{force(F)} \over {mass(m)}}$

$\Rightarrow$ a = ${{qE} \over m}$ [ $\because$ F = qE]

= ${{8 \times {{10}^{ - 6}} \times 100} \over {{{10}^{ - 3}}}}$ = 0.8 ms ^{$-$ 2}

As per question, when electric field is switched on, the body strikes to the wall and then returns back.

For one oscillation,

s = ut + ${1 \over 2}$ at²

$\Rightarrow$ 0.1 = ${1 \over 2}$ $\times$ 0.8 t² [ $\because$ u = 0]

$\Rightarrow$ 0.2 = 0.8 t²

$\Rightarrow$ ${2 \over 8}$ = t² $\Rightarrow$ t² = ${1 \over 4}$ $\Rightarrow$ t = ${1 \over 2}$

$\therefore$ Time period = 2 $\times$ ${1 \over 2}$ = 1 s

Therefore, if the collision of the body is perfectly elastic, the time period of motion will be 1s.