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)
Torque on a spanner at an angle
A force of 120 N is applied at the end of a 25 cm spanner at 60° to the handle.
τ = r F sin θ = 0.25 × 120 × sin 60° = 0.25 × 120 × 0.866
τ = 26 N·m (at 90° it would be 30 N·m — the maximum)
Balancing a see-saw (principle of moments)
A 40 kg child sits 1.5 m left of the pivot; a 30 kg child sits on the right at distance d. (g = 10 m/s²)
Στ = 0 → 400 × 1.5 = 300 × d → 600 = 300 d
d = 2.0 m — the lighter child sits farther from the pivot
Reactions of a beam on two supports
A uniform 6 m beam weighing 200 N rests on end supports A and B; a 450 N load sits 2 m from A.
1st condition: R_A + R_B = 650 N
2nd condition (torques about A): R_B × 6 = 450 × 2 + 200 × 3 = 1500
R_B = 250 N; R_A = 650 − 250 = 400 N (the support nearer the load carries more)
Angular kinematics of a braking wheel
A wheel at ωi = 60 rad/s is brought to rest uniformly in 12 s.
α = (0 − 60)/12 = −5 rad/s²
2αθ = ωf² − ωi² → θ = (0 − 3600)/(2 × −5) = 360 rad
revolutions = 360/2π ≈ 57.3 rev