The position vector \( \vec{r} \) of a particle of mass \( m \) is given by the following equati...
0The position vector \( \vec{r} \) of a particle of mass \( m \) is given by the following equation \( \vec{r}(t)=\alpha t^{3} i+\beta t^{2} \hat{j} \), where
\( \mathrm{P} \) \( \alpha=\frac{10}{3} \mathrm{~ms}^{-3}, \beta=5 \mathrm{~ms}^{-2} \) and \( m=0.1 \mathrm{~kg} \). At \( t=1 \mathrm{~s} \), which
W of the following statement(s) is(are) true?
(1) The velocity \( \vec{v} \) is given by \( \vec{v}=(10 \hat{i}+10 \hat{j}) \mathrm{ms}^{-1} \)
(2) The angular momentum \( \vec{L} \) with respect to the origin is given by \( \vec{L}=-\left(\frac{5}{3}\right) \hat{k} \mathrm{Nms} \)
(3) The force \( \vec{F} \) is given by \( \vec{F}=(\hat{i}+2 \hat{j}) \mathrm{N} \)
(4) The torque \( \vec{\tau} \) with respect to the origin is given by \( \vec{\tau}=-\left(\frac{20}{3}\right) \hat{k} \mathrm{Nm} \)
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