Govt. Exams
Entrance Exams
Newton's first law states that an object at rest remains at rest unless acted upon by an external force - this is the law of inertia.
Vertical component = F sin(60°) = 50 × (√3/2) = 50 × 0.866 = 43.3 N
Mass is a scalar quantity as it has magnitude only, not direction. Displacement, velocity, and acceleration are vectors.
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
