Govt. Exams
Entrance Exams
Using h = ½gt², 80 = ½(10)t², t² = 16, t = 4 seconds
Angular displacement = 5 × 2π = 10π radians. Time = 10 seconds. Angular velocity ω = 10π/10 = π rad/s
Net acceleration = √(aₓ² + aᵧ²) = √(3² + 4²) = √(9 + 16) = √25 = 5 m/s²
On a frictionless incline: a = g sin θ = 10 × sin(30°) = 10 × 0.5 = 5 m/s²
Using Newton's second law: T - mg = ma. T = m(g + a) = 1000(10 + 2) = 1000 × 12 = 12000 N
Centripetal acceleration aᶜ = v²/r = (20)²/5 = 400/5 = 80 m/s²
Initial velocity u = 18 km/h = 5 m/s. Final velocity v = 54 km/h = 15 m/s. Time t = 8 s. Using a = (v - u)/t = (15 - 5)/8 = 10/8 = 1.25 m/s²
Option C is the statement of Newton's second law (F = ma), not the first law. Newton's first law deals with inertia and absence of acceleration.
Using v² = u² + 2as, where u = 0, a = 10 m/s², s = 80 m. v² = 0 + 2(10)(80) = 1600, so v = 40 m/s
72 km/h = 20 m/s. Using v = u - at, 0 = 20 - 5t, so t = 4 seconds.
