NEET UG PHYSICS MCQ: SYSTEM OF PARTICLES

The position vectors of two 1 kg particles, (A) and (B), are given by $\overrightarrow{\mathrm{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{\mathrm{i}}+\alpha_2 \text{t}\hat{\mathrm{j}}+\alpha_3 \text{t} \hat{\mathrm{k}}\right) \mathrm{m}$ and $\overrightarrow{\mathrm{r}}_{\mathrm{B}}=\left(\beta_1 \mathrm{t} \hat{\mathrm{i}}+\beta_2 \mathrm{t}^2 \hat{\mathrm{j}}+\beta_3 \mathrm{t} \hat{\mathrm{k}}\right) \mathrm{m},$ respectively; $\left(\alpha_1=1 \mathrm{~m} / \mathrm{s}^2, \alpha_2=3 \mathrm{~nm} / \mathrm{s}, \alpha_3=2 \mathrm{~m} / \mathrm{s}, \beta_1=2 \mathrm{~m} / \mathrm{s},\beta_2=-1 \mathrm{~m} / \mathrm{s}^2, \beta_3=4 \mathrm{p} \mathrm{m} / \mathrm{s}\right),$ where t is time, n and p are constants, At $\text{t}=1 \mathrm{~s},$ $\left|\overrightarrow{\mathrm{V}}_{\mathrm{A}}\right|=\left|\overrightarrow{\mathrm{V}}_{\mathrm{B}}\right|$ and velocities $\mathrm{\vec{V}_A}$ and $\mathrm{\vec{V}_B}$ of the particles are orthogonal to each other. At $\text{t}=1 \mathrm{~s},$ the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is $\sqrt{\mathrm{L}} \mathrm{~kgm}^2 \mathrm{~s}^{-1}.$ The value of 'L' is