The potential energy of a particle of mass at a distance from a fixed point is given by

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

The potential energy of a particle of mass

m

at a distance

r

from a fixed point

O

is given by

V(r) = kr^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? [Adv. 2018] (1)

v = \sqrt{\frac{k}{2m}}R

(2)

v = \sqrt{\frac{k}{m}}R

(3)

L = \sqrt{mk}R^2

(4)

L = \sqrt{\frac{mk}{2}}R^2