VCM — Rigid Rod & Spherical Shell — IISER Physics MCQs with Solutions
Free IISER Physics VCM — Rigid Rod & Spherical Shell MCQs with step-by-step solutions (8 questions). Part of Circular Motion. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — VCM — Rigid Rod & Spherical Shell · easy · theory
For a mass fixed to a light RIGID ROD moving in a vertical circle, the minimum speed at the topmost point is:
A. √(5gr)
B. √(2gr)
C. √(gr)
D. Zero ✓ Correct
Solution: A rod can PUSH as well as pull, so it can support the mass at the top; v_top can be zero.
Q2 — VCM — Rigid Rod & Spherical Shell · medium · theory
The minimum speed at the BOTTOM for a rod-mounted mass to complete a vertical circle of radius r is:
A. √(gr)
B. √(2gr)
C. √(5gr)
D. √(4gr) = 2√(gr) ✓ Correct
Solution: With v_top = 0: ½mv_b² = mg(2r) ⇒ v_b = √(4gr). Trap: √(5gr) applies to strings, not rods.
Q3 — VCM — Rigid Rod & Spherical Shell · easy · numerical
A mass on a rigid rod just completes a vertical circle of radius 2.5 m. Its speed at the lowest point is:
A. ≈ 11.2 m/s
B. 5 m/s
C. √50 m/s
D. 10 m/s ✓ Correct
Solution: v_b = √(4gr) = √100 = 10 m/s.
Q4 — VCM — Rigid Rod & Spherical Shell · medium · numerical
A 2 kg mass on a rod is at rest at the top of a vertical circle (r = 1 m). The force exerted by the rod there is:
A. Zero
B. 20 N compression (pushing up) ✓ Correct
C. 20 N tension
D. 40 N tension
Solution: At rest, no centripetal need: the rod simply supports the weight — a compressive (pushing) force of mg = 20 N. A string could never do this.
Q5 — VCM — Rigid Rod & Spherical Shell · hard · numerical
A particle slides inside a smooth SPHERICAL SHELL of radius r, starting from the top edge... For a particle sliding inside a vertical circular shell released from the level of the centre, its speed at the lowest point is:
A. √(2gr) ✓ Correct
B. √(gr)
C. √(5gr)
D. 2√(gr)
Solution: Falls through height r: v = √(2gr). The shell's normal reaction (like tension) does no work.
Q6 — VCM — Rigid Rod & Spherical Shell · medium · numerical
A ball inside a smooth spherical shell of radius 1 m circles vertically, just maintaining contact at the top. Its speed at the top is:
A. Zero
B. 10 m/s
C. √50 m/s
D. √10 ≈ 3.2 m/s ✓ Correct
Solution: The shell's inner wall can only push inward — same critical condition as a string: N = 0, v = √(gr) = √10 m/s.
Q7 — VCM — Rigid Rod & Spherical Shell · hard · theory
A ball circles inside a smooth spherical shell in a vertical plane. Compared with a string of the same radius, the critical (minimum) condition at the top is:
A. Like a rod: v_top can be zero
B. No minimum exists
C. Twice as demanding
D. Identical — the shell's inward normal force plays exactly the role of the string tension ✓ Correct
Solution: The inner wall can only push toward the centre (like tension pulling inward), so N = 0 at the top gives the same v_top = √(gr) criterion. A ball on the OUTSIDE of a sphere is the opposite case.
Q8 — VCM — Rigid Rod & Spherical Shell · hard · numerical
A 1 kg ball on a rigid rod completes a vertical circle (r = 1 m) with v_bottom = 8 m/s. Its speed at the top is:
A. √24 ≈ 4.9 m/s ✓ Correct
B. √44 m/s
C. 8 m/s
D. 2 m/s
Solution: v_t² = v_b² − 4gr = 64 − 40 = 24 ⇒ v_t ≈ 4.9 m/s (energy conservation; the rod does no work).