VCM — Rigid Rod & Spherical Shell — JEE Main Physics MCQs with Solutions
Free JEE Main 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. √(gr)
B. √(5gr)
C. Zero ✓ Correct
D. √(2gr)
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. √(5gr)
B. √(gr)
C. √(4gr) = 2√(gr) ✓ Correct
D. √(2gr)
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. 5 m/s
B. ≈ 11.2 m/s
C. 10 m/s ✓ Correct
D. √50 m/s
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. 40 N tension
B. 20 N compression (pushing up) ✓ Correct
C. 20 N tension
D. Zero
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. √(gr)
B. √(2gr) ✓ Correct
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. √10 ≈ 3.2 m/s ✓ Correct
B. √50 m/s
C. 10 m/s
D. Zero
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 · numerical
A rod-mounted mass barely completes a vertical circle (v_top ≈ 0, r = 1 m, m = 1 kg). The rod's force on the mass at the TOP is:
A. 10 N pushing outward/up (compression) ✓ Correct
B. Zero
C. 20 N compression
D. 10 N pulling (tension)
Solution: With v_top → 0, the needed centripetal force → 0; the rod must hold the weight: a 10 N compressive force. In a string this is impossible — the loop would fail.
Q8 — VCM — Rigid Rod & Spherical Shell · medium · numerical
A particle inside a smooth spherical shell (r = 2 m) leaves the surface... A particle slides from the TOP OUTSIDE of a smooth sphere of radius 2 m. It leaves the surface after descending a height of:
A. 1 m
B. 4/3 m
C. 2/3 m ✓ Correct
D. 2 m
Solution: Leaves when mg cosθ = mv²/r with v² = 2gh and h = r(1−cosθ) ⇒ cosθ = 2/3 ⇒ h = r/3 = 2/3 m — the classic sphere-departure result.