Physics - Center of Mass Question with Solution | TestHub
A uniform circular disc of radius has a circular hole of radius cut out. The center of the hole is at a distance from the center of the original disc. Another identical disc of radius is placed such that its center is at a distance from the center of the original disc, on the opposite side of the hole. All centers are collinear. Let the original disc's center be the origin and the centers lie along the x-axis. Assume mass per unit area is . Match the following quantities related to the center of mass (COM):
List - I | List - II |
|---|---|
(P) x-coordinate of the COM of the disc with the hole | (1) |
(Q) y-coordinate of the COM of the disc with the hole | (2) |
(R) x-coordinate of the COM of the entire system (disc with hole + added disc) | (3) |
(S) y-coordinate of the COM of the entire system (disc with hole + added disc) | (4) |
Options:
Answer:
Solution:
The mass of the original disc is with COM at . The hole has mass with COM at . The disc with hole has mass . Its x-coordinate is . Its y-coordinate . So (P)-(2), (Q)-(1). The added disc has mass with COM at . The total system mass is . Its x-coordinate is . Its y-coordinate . So (R)-(3), (S)-(1).
