A uniform circular disc of radius 50 cm at rest is free

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A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s^–2. Its net acceleration in ms^–2 at the end of 2.0s is approximately :

1. 8.0
2. 7.0
3. 6.0
4. 3.0

Correct Option: A

Given: Radius of disc, R = 50 cm
angular acceleration α = 2.0 rads^–2; time t = 2s
Particle at periphery (assume) will have both radial (one) and tangential acceleration
a_t = Rα = 0.5 × 2 = 1 m/s²
From equation, ω = ω₀ + αt
ω = 0 + 2 × 2 = 4 rad/sec
a_c = ω²R = (4)² × 0.5 = 16 × 0.5 = 8m/s²
Net acceleration,
a_total = √a_t² + a_c² = √1² + 8² ≈ 8 m/s²