A particle moves in a circle at angular speed ω=√2 rad/s about the line x=y/2=z/2. At point (2,3,5) m, find speed (m/s).
Physics · Mixed Chapter
JEE Main Practice

Question

A particle moves in a circle at angular speed ω=√2 rad/s about the line x=y/2=z/2. At point (2,3,5) m, find speed (m/s).

G1 Physics · Accepted Answer

Step 1: The rotation axis has direction vector (1,2,2) and unit vector n̂=(1,2,2)/3. Step 2: Position vector r⃗=(2,3,5). Its perpendicular distance squared from axis is d²=|r⃗|²−(r⃗·n̂)². Step 3: |r⃗|²=4+9+25=38; r⃗·n̂=(2+6+10)/3=6 ⇒d²=38−36=2. Step 4: d=√2 m and v=ωd=√2×√2=2 m/s.