JEE Main 2025 Apr 4 Shift 1, Physics Q11: Newton's Laws Of Motion

Differentiating $\vec{r}$ twice with respect to time gives $\vec{a}=-{\omega }^2(a\hat{i}\cos \omega t+a\hat{j}\sin \omega t)=-{\omega }^2\vec{r}$.

The motion is therefore uniform circular motion of radius $a$ (centripetal acceleration directed radially inward). By Newton's second law $\vec{F}=m\vec{a}=-m{\omega }^2\vec{r}$, so $\vec{F}$ points opposite to $\vec{r}$.