A bead slides down a vertical rod fixed inside a train accelerating horizontally at 4 m s⁻². The rod length is 1 m and μ = 1/2. If the time to reach the bottom is n/2 s, find n. Take g = 10 m s⁻².
Physics · Newtons law of motion and Friction · friction and single block problem
JEE Mains

Question

A bead slides down a vertical rod fixed inside a train accelerating horizontally at 4 m s⁻². The rod length is 1 m and μ = 1/2. If the time to reach the bottom is n/2 s, find n. Take g = 10 m s⁻².

Physics · Newtons law of motion and Friction · friction and single block problem

G1 Physics · Accepted Answer

In the train frame, horizontal pseudo force gives normal N = m×4. Friction upward is μN = 2m. Net downward force is m(10-2), so vertical acceleration is 8 m s⁻². From 1 = ½(8)t², t=0.5 s = n/2, hence n=1.