COM of Continuous Bodies — IISER Physics MCQs with Solutions
Free IISER Physics COM of Continuous Bodies MCQs with step-by-step solutions (8 questions). Part of Centre of Mass, Momentum & Collisions. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — COM of Continuous Bodies · easy · theory
The centre of mass of a uniform semicircular RING of radius R lies on the symmetry axis at a distance from the centre of:
A. 4R/3π
B. 2R/π ✓ Correct
C. R/2
D. R/π
Solution: Standard results: semicircular ring 2R/π; semicircular DISC 4R/3π — don't swap them.
Q2 — COM of Continuous Bodies · medium · theory
The COM of a uniform solid HEMISPHERE of radius R lies above the flat face at:
A. R/2
B. 3R/8 ✓ Correct
C. 2R/π
D. 3R/5
Solution: Solid hemisphere: 3R/8. (Hollow hemispherical shell: R/2; solid cone: h/4 above the base.)
Q3 — COM of Continuous Bodies · easy · numerical
A uniform rod of length 2 m has its centre of mass at a distance from one end of:
A. 0.5 m
B. 1 m ✓ Correct
C. 2/3 m
D. 1.5 m
Solution: A uniform rod's COM is at its midpoint: L/2 = 1 m.
Q4 — COM of Continuous Bodies · medium · numerical
A rod of length 1 m has linear density λ = 2x (kg/m). The COM from the light end (x = 0) is at:
A. 2/3 m ✓ Correct
B. 1/3 m
C. 3/4 m
D. 1/2 m
Solution: x_cm = ∫xλdx/∫λdx = (∫2x²)/(∫2x) = (2/3)/(1) = 2/3 m — shifted towards the heavy end.
Q5 — COM of Continuous Bodies · hard · numerical
A uniform solid CONE of height 12 cm stands on its base. Its centre of mass is above the base at:
A. 4 cm
B. 3 cm ✓ Correct
C. 8 cm
D. 6 cm
Solution: COM of a solid cone is h/4 above the base = 3 cm (or 3h/4 below the apex).
Q6 — COM of Continuous Bodies · medium · numerical
A uniform semicircular disc has radius 21 cm (π ≈ 22/7). Its COM lies above the centre at 4R/3π =
A. ≈ 8.9 cm ✓ Correct
B. ≈ 10.5 cm
C. ≈ 13.4 cm
D. ≈ 6.7 cm
Solution: 4R/3π = 4×21/(3×22/7) = 84×7/66 ≈ 8.9 cm.
Q7 — COM of Continuous Bodies · hard · theory
For a uniform triangular lamina, the centre of mass coincides with the:
A. Incentre always
B. Orthocentre
C. Circumcentre
D. Centroid (intersection of the medians) ✓ Correct
Solution: Strips parallel to a side have their centres on the median: the COM is the centroid, at 2/3 of each median from the vertex.
Q8 — COM of Continuous Bodies · hard · numerical
A hollow hemispherical SHELL and a SOLID hemisphere of the same radius R rest on their flat faces. The ratio of their COM heights (shell : solid) is:
A. 1 : 1
B. 4 : 3 ✓ Correct
C. 16 : 9
D. 3 : 4
Solution: Shell: R/2; solid: 3R/8. Ratio = (R/2)/(3R/8) = 4/3.