A particle moves on a circular path of radius 0.2m with an angular acceleration 0.25 rad/s². The particle starts from rest at t = 0. The time at which magnitude of radial acceleration and tangential acceleration are same is _________ sec.
Physics · Mixed Chapter
JEE Mains

Question

A particle moves on a circular path of radius 0.2m with an angular acceleration 0.25 rad/s². The particle starts from rest at t = 0. The time at which magnitude of radial acceleration and tangential acceleration are same is _________ sec.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Tangential acceleration is aₜ=αr. Radial acceleration is aᵣ=ω²r. Step 2: Particle starts from rest under constant angular acceleration α=0.25 rad s⁻²; therefore ω=αt. Step 3: Equate aᵣ=aₜ: (αt)²r=αr, so αt²=1. Step 4: t=1/√α=1/√0.25=2 s. Answer: 2.