Physics - Rotation Question with Solution | TestHub

$\overrightarrow{r}=\alpha t^3\widehat{i}+\beta t^2\widehat{j}$
$\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}=3\alpha t^2\widehat{i}+2\beta t\widehat{j}$
$\overrightarrow{a}=\frac{d^2\overrightarrow{r}}{d{t}^2}=6\alpha t\widehat{i}+2\beta \widehat{j}$
At t = 1
(i)$\overrightarrow{v}=3\times \frac{10}{3}\times 1\widehat{i}+2\times J\times 1\widehat{j}$
$=10\widehat{i}+10\widehat{j}$
(ii)$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$
$=\left(\frac{10}{3}\times 1\widehat{i}+5\times 1\widehat{j}\right)\times 0.1\left(10\widehat{i}+10\widehat{j}\right)$
$= -\frac{5}{3}\widehat{k}$
(iii)$\overrightarrow{F}=m\times \left(6\times \frac{10}{3}\times 1\widehat{i}+2\times 5\widehat{j}\right)=2\widehat{i}+\widehat{j}$
(iv)$\overrightarrow{\tau }=r\times \overrightarrow{F}$
$=\left(\frac{10}{3}\widehat{i}+5\widehat{j}\right)\times \left(2\widehat{i}+\widehat{j}\right)$
$=+\frac{10}{3}\widehat{k}+10\left(-\widehat{k}\right)$
$=-\frac{20}{3}\widehat{k}$