$ r(t)=\alpha t^3 \hat{i}+\beta t^2 \hat{j} $
Given, $\alpha=10 / 3 \mathrm{~m} / \mathrm{s}^3, \beta=5 \mathrm{~m} / \mathrm{s}^2, \mathrm{~m}=0.1 \mathrm{~kg}$; at $\mathrm{t}=1 \mathrm{~s}$
$ \begin{aligned} & \vec{v}=\alpha\left(3 t^2\right) \hat{i}+2 \beta t \hat{j} \\ & \vec{v}=(10 \hat{i}+10 \hat{j}) \\ & \frac{d \vec{v}}{d t}=\vec{a}=6 \alpha t \hat{i}+2 \beta \hat{j} \\ & \vec{F}=m \vec{a}=0.1[6 \alpha t \hat{i}+2 \beta \hat{j}] \end{aligned} $
$\begin{aligned} & =2 \hat{\mathrm{i}}+\hat{\mathrm{j}} \\ & \mathrm{m}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{v}}) \\ & \overrightarrow{\mathrm{i}}=-\frac{5}{3} \hat{\mathrm{k}} \mathrm{Nms} \\ & \vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}} \\ & =\left(\alpha t^3 \hat{\mathrm{i}}+\beta t^2 \hat{\mathrm{j}}\right) \times \mathrm{m}(6 \alpha t \hat{\mathrm{i}}+2 \beta t \hat{\mathrm{j}}) \\ & =\mathrm{m}\left(2 \alpha \beta t^3 \hat{\mathrm{k}}-6 \alpha \beta t^3 \hat{\mathrm{k}}\right) \\ & =\frac{-20}{3} \hat{\mathrm{k}} \mathrm{Nm}\end{aligned}$