The position of an object having mass \( 0.1 \,\text{kg} \) as a function of time \( t \) is given as \( \vec{r}=(10t^{2}\hat{\imath}+5t^{3}\hat{\jmath})\,\text{m} \). At \( t=1\,\text{s} \), which of the following statements are correct?
A. The linear momentum \( \vec{p}=(2\hat{\imath}+1.5\hat{\jmath})\,\text{kg}\cdot\text{m}/\text{s} \)
B. The force acting on the object \( \vec{F}=(2\hat{\imath}+3\hat{\jmath})\,\text{N} \)
C. The angular momentum of the object about its origin \( \vec{L}=15\hat{k}\,\text{J}\,\text{s} \)
D. The torque acting on the object about its origin \( \vec{\tau}=20\hat{k}\,\text{N}\,\text{m} \)
Choose the correct answer from the options given below:
