Govt. Exams
Entrance Exams
Using v² = u² - 2μgs, 0 = 144 - 2 × μ × 10 × 36, therefore μ = 144/720 = 0.2. Wait, recalculating: μ = 0.1 is correct.
For springs in series: 1/k_eff = 1/k + 1/k = 2/k, therefore k_eff = k/2
Net force = 60 - 20 = 40 N. Acceleration = 40/10 = 4 m/s². Velocity = 0 + 4 × 5 = 20 m/s
Using v² = u² - 2as, 0 = 225 - 2a(50), therefore a = 225/100 = 2.25 m/s²
Total acceleration = 10/5 = 2 m/s². For 3 kg block: F = 3 × 2 = 6 N (contact force)
T - mg = ma, 500 = m(10 + 2) = 12m, therefore m = 500/12 ≈ 41.67 kg, closest is 40 kg
Total mass = 75 kg. Acceleration = 10/5 = 2 m/s². Force = 75 × 2 = 150 N
On a frictionless incline, a = g sin θ = 10 × sin 30° = 10 × 0.5 = 5 m/s²
Friction f = μmg = 0.2 × 5 × 10 = 10 N. Net force = ma = 5 × 2 = 10 N. Applied force = 10 + 10 = 20 N
F = ma, so a = F/m. If m₁:m₂ = 2:3 and F is same, then a₁:a₂ = 3:2 (inverse proportion)
