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)
Work done by a force at an angle
A man pulls a crate 8 m with a 50 N rope at 60° to the horizontal.
W = Fd cos θ = 50 × 8 × cos 60° = 50 × 8 × 0.5 = 200 J
Only the horizontal component (25 N) does work; the vertical component does none.
Speed of a falling body by energy conservation
A 0.3 kg mango falls from h = 4.9 m (g = 9.8 m/s²).
mgh = ½mv² → v = √(2gh) = √(2 × 9.8 × 4.9) = √96.04 = 9.8 m/s
The mass cancels — any body falls to the same speed from the same height.
Power of a pump with efficiency
A pump lifts 200 kg of water per minute through 7 m; efficiency 70% (g = 9.8 m/s²).
useful power = mgh/t = (200 × 9.8 × 7)/60 ≈ 228.7 W
input power = useful ÷ efficiency = 228.7 / 0.70 ≈ 327 W
Energy on the electricity bill (kWh)
A 1.5 kW air-conditioner runs 6 h/night for 30 nights.
E = P × t = 1.5 kW × 180 h = 270 kWh (units)
in joules: 270 × 3.6 × 10⁶ = 9.72 × 10⁸ J
Work–energy theorem: stopping a car
A 1000 kg car at 15 m/s brakes with a 5000 N friction force.
W(net) = ΔKE → −5000 × d = 0 − ½ × 1000 × 15² = −112 500 J
d = 112 500 / 5000 = 22.5 m