A particle slides down on a smooth incline of inclination 30 o , fixed in an elevator going up with an acceleration 2 m / s 2 . The box of incline has width 4m. The time taken by the particle to reach the bottom will be

Step-by-step solution

In the frame of elevator, a = acceleration of the particle with respect to the elevator ∴ m sin ⁡ 30 g + 2 = m a a = g + 2 sin ⁡ 30 o = 10 + 2 . 1 2 = 6 m / s 2 ∴ The distance travelled by the particle from the top to the bottom, d = 4 cos ⁡ 30 o = 4 3 2 = 8 3 3 m Using s = u t + 1 2 a t 2 , 8 3 3 = 0 × t + 1 2 6 t 2 ⇒ t 2 = 16 3 3 × 6 ∴ t = 4 3 3 2 s