A 1 kg block is thrown horizontally at 10 m s⁻¹ on a stationary 2 kg plank. μ = 0.5 and the plank is on a frictionless floor. The time to reach no relative motion is n/3 s. Find n.
Physics · Newtons law of motion and Friction · friction and single block problem
JEE Mains

Question

A 1 kg block is thrown horizontally at 10 m s⁻¹ on a stationary 2 kg plank. μ = 0.5 and the plank is on a frictionless floor. The time to reach no relative motion is n/3 s. Find n.

G1 Physics · Accepted Answer

Kinetic friction is 5 N. Block acceleration is -5 m s⁻²; plank acceleration is +5/2 = 2.5 m s⁻². Relative acceleration magnitude is 7.5 m s⁻². Time to reduce relative speed from 10 to zero is 10/7.5 = 4/3 s, hence n=4.