The potential energy of a particle of mass m at a distance r from a fixed point O is given by $V (r) = k \frac{r^{2}}{2}$ .where 𝑘 is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If 𝑣 is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true?

Question

Infinity Learn · Accepted Answer

$$V=kr22F=-dVdr=$$−kr                             At $$r=R$$,$$kR=mv2R(Centripetal$$ $$force)$$                        $$v=kR2m=kmR$$​Angular $$Momentum=L=mvR=mkmR2=mkR2$$

Column-A		Column-B
(a)	Acceleration of body	(p)	Changes direction but constant in magnitude
(b)	Friction force on body	(q)	Changes magnitude but constant in direction
(c)	Angular momentum of the particle	(r)	Changes direction as well as magnitude
(d)	Normal force by table	(s)	Direction as well as the magnitude is constant

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