Board-style MCQs and past-paper numericals in the BIEK / Sindh Board pattern. Tap an option to check yourself instantly. Solved questions are at the bottom.
Multiple-choice questions
Solved numericals (past papers)
rpm → rad/s and the speed of a rim point
A wheel turns at 90 rpm; a point lies 0.5 m from the axis.
ω = 90 × 2π/60 = 3π = 9.42 rad/s
v = rω = 0.5 × 9.42 = 4.71 m/s
Friction providing the centripetal force on a flat curve
m = 1000 kg, r = 100 m, v = 20 m/s, g = 9.8 m/s².
F = mv²/r = 1000 × 400/100 = 4 000 N
minimum μ = F/(mg) = 4000/9800 ≈ 0.41 — a wet road (μ ≈ 0.3) cannot supply it: slow down.
Banking angle of a curve
r = 200 m, v = 72 km/h = 20 m/s.
tan θ = v²/(rg) = 400/(200 × 9.8) = 0.204
θ = tan⁻¹(0.204) ≈ 11.5° — independent of the vehicle's mass.
Tension at the top and bottom of a vertical circle
m = 0.4 kg, r = 0.8 m, v = 4 m/s (constant), g = 9.8 m/s².
mv²/r = 0.4 × 16/0.8 = 8.0 N · mg = 3.92 N
T(top) = 8.0 − 3.92 = 4.08 N · T(bottom) = 8.0 + 3.92 = 11.92 N
Minimum speed at the top of a whirled bucket
r = 1.0 m, g = 9.8 m/s². At minimum speed the tension (and the bucket's push on the water) is zero — gravity alone supplies mv²/r.
mg = mv²/r → v = √(gr) = √9.8 = 3.13 m/s (≈ 30 rev/min — an easy arm swing).