If L and P represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector as r = a(icos ω t + jsin ω t). The direction of force is (a) Opposite to the direction of L (b) Opposite to the direction of L × P (c) Opposite to the direction of r (d) Opposite to the direction of P

Answer: (c). r=a(cos ω t i+sin ω t j) is uniform circular motion. F=m r=-mω² r So the force is directed opposite to r (towards the centre). So the answer is (c).

If L and P represent the angular momentum and linear momentum… | JEE Main 2025 (4 Apr, Shift 1)

Q16JEE Main 2025 · 4 APR · SHIFT 1Medium

Angular Momentum & its Conservation

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector as $\vec{r} = a\left(\hat{i}\cos\omega t + \hat{j}\sin\omega t\right)$ . The direction of force is

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Answer: (c)

$\vec r=a(\cos\omega t\,\hat i+\sin\omega t\,\hat j)$ is uniform circular motion.
$\vec F=m\ddot{\vec r}=-m\omega^2\vec r$
So the force is directed opposite to $\vec r$ (towards the centre).
So the answer is (c).

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