Govt. Exams
N - mg = ma (upward acceleration), so N = m(g + a) = 60(10 + 2) = 60 × 12 = 720 N
Centripetal force F = ma_c = 2 × 8 = 16 N. This is the net force directed toward the center of circular motion.
At 45°, vertical component = 20sin(45°) = 10√2 m/s. Using v² = u² - 2gh, at max height v=0: h = u²/(2g) = (10√2)²/(2×10) = 200/20 = 10 m
Maximum velocity in SHM = ωA = 4 × 0.5 = 2 m/s
Net force = (3-3)i + (4-4)j = 0i + 0j = 0 N. The magnitude is 0 N.
Using energy conservation: mgh = ½mv². v = √(2gh) = √(2×10×5) = √100 = 10 m/s
The moment of inertia of a uniform disc about its central perpendicular axis is I = ½MR²
Centripetal acceleration = v²/r = 25/10 = 2.5 m/s²
a = g sin(30°) = 10 × 0.5 = 5 m/s²
Using v² = u² - 2gh, at maximum height v = 0. So 0 = 1600 - 2(10)h, h = 80 m