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JEE Main 2025 Jan 23 Shift 1, Physics Q20: Centre of Mass

JEE Main2025Jan 23, Shift 1Physics
Q.

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of a radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be-

  1. A

    cm

  2. B

    cm

  3. C

    cm

  4. D

    cm

Solution

Treat the residual disc as the full disc minus the cut-out disc.

Let be the surface mass density and write masses in units of (full disc mass). The cut-out has radius 5, so its area is of the full disc and its mass is .

The hole's edge touches the outer rim, so its centre is at distance cm from the origin (along, say, the +x direction). Place the full disc's CoM at the origin.

Using the 'subtract' rule for CoM:

cm.

Distance from origin cm.

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