Verified Solution • 2025–26 Session moderate

Q6.15: NCERT Physics - Part 1 SYSTEMS OF PARTICLES AND ROTATIONAL MOTION 6.15 Solution: From a uniform disk of radius R, a circular hole of radius R/2…

From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of the original disc. Locate the centre of gravity of the resulting flat body.

Step-by-Step Verified Solution

**Answer:** The centre of mass shifts by R/6R/6 from the centre of the original disc, on the diametrically opposite side to the hole. **Step-by-Step Explanation:** Using negative mass method: - Mass of original disc: M=πR2σM = \pi R^2 \sigma - Mass of hole: M′=π(R/2)2σ=M/4M' = \pi (R/2)^2 \sigma = M/4 Taking the centre of original disc at origin:
xCM=M(0)−(M/4)(R/2)M−M/4=−MR/83M/4=−R6x_{CM} = \frac{M(0) - (M/4)(R/2)}{M - M/4} = \frac{-MR/8}{3M/4} = -\frac{R}{6}
The negative sign indicates the shift is away from the hole [citation:28].

All Questions in this Chapter

Q6.1 Q6.2 Q6.3 Q6.4 Q6.5 Q6.6 Q6.7 Q6.8 Q6.9 Q6.10 Q6.11 Q6.12 Q6.13 Q6.14 Q6.15 Q6.16 Q6.17

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