a
As shown, the time after which velocity of particle becomes antiparallel is :
$\mathrm{T}=2 \mathrm{t}_{1}+2 \mathrm{t}_{2}$
$=2\left(\frac{\theta}{\omega}\right)+2\left(\frac{\mathrm{R}}{\mathrm{v}}\right)=2\left[\frac{\pi / 4}{\mathrm{qB} / \mathrm{m}}\right]+2\left[\frac{\mathrm{m}}{\mathrm{qB}}\right]$
$=\frac{\mathrm{m} \pi}{2 \mathrm{qB}}+\frac{2 \mathrm{m}}{\mathrm{qB}}=\frac{\mathrm{m}}{2 \mathrm{qB}} [\pi+4]$
