Question

(a) A circular ring has radius r and mass M. Let L be the axis of the ring (the line that is perpendicular to the plane of the ring and that passes through the center of the ring). What is the force on a mass m that is located on L, at a distance x from the center of the ring?

(b) A hole with radius R is cut out from an innite at sheet with mass density (kg=m2). What is the force on a mass m that is located on the analogously dened line L, at a distance x from the center of the hole? Hint: Consider the plane to consist of many concentric rings, and integrate over the rings.

(c) If a particle is released from rest on L, very close to the center of the hole, show that it undergoes oscillatory motion. Find the frequency of these oscillations.

(d) If a particle is released from rest on L, at a distance x from the sheet, what is its speed when it passes through the center of the hole? What does your answer reduce to for large x (or equivalently, small R)?

Answer 1