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NEETPhysicsCenter of Mass, Momentum and Collision

Match the following columns with respective positions of centre of mass - ( array |l|l|l|l| & Column - I & & Column - II (A) & uniform rod length = R & (P) & x = 3 R 8 (B) & array l uniform thin semicircular ring of radius R array & (Q) & x = R 2 (C) & array l unifiorm semicurcula disc of radius R array & (R) & x = 4 R 3 (D) & array l uniform solid hemisphere of radius R array & (S) & x = 2 R array )

Options

  1. A(A: P, B: R, C: Q, D: S )
  2. B(A: Q, B: P, C: R, D: S )
  3. C(A: Q, B: S, C: R, D: P )
  4. D(A:S, B:P, C:Q, D:R )

Correct answer

C. (A: Q, B: S, C: R, D: P )

Step-by-step solution

(A) Uniform rod of length (R ) - For a uniform rod, the COM lies exactly at the midpoint. So, (x= R 2 ). That matches (Q). (B) Uniform thin semicircular ring of radius R - Standard result: COM of a semicircular ring lies at a distance ( 2 R ) from the center, along symmetry axis. So, (x= 2 R ). That matches (S). (C) Uniform semicircular disc of radius R - Standard result: COM of a semicircular lamina is at a distance ( 4 R 3 ) from the center along symmetry axis. So, (x= 4 R 3 ). That matches (R). (D) Uniform solid

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