Q 11-03-176JEE MainJEE Main 2025 (4 Apr, Shift 1)Easy
If $\vec L$ and $\vec P$ represent the angular momentum and linear momentum respectively of a particle of mass $m$ having position vector $\vec r = a(\hat i\cos\omega t + \hat j\sin\omega t)$, the direction of the force is:
Answer: (A) Opposite to the direction of $\vec r$
The particle moves uniformly on a circle of radius $a$. Differentiating twice:
$$\vec a = \frac{d^2\vec r}{dt^2} = -\omega^2\vec r$$
So $\vec F = m\vec a = -m\omega^2\vec r$, directed opposite to $\vec r$ (towards the centre).
(For comparison: $\vec L$ is along $\hat k$, perpendicular to $\vec F$; $\vec P$ is tangential; and $\vec L\times\vec P$ points towards the centre, i.e. along $\vec F$, not opposite to it.)
Solution by Sreeraj P, M.Sc Physics