JEE Main 2026 — Center of Mass Momentum and Collision Question with Solution

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