A solid billiard ball of radius R is struck by a purely horizontal cue impulse at height h above its centre. For immediate rolling without slipping, h=yR/5. Find y.
Physics · Mixed Chapter
JEE Main Practice

Question

A solid billiard ball of radius R is struck by a purely horizontal cue impulse at height h above its centre. For immediate rolling without slipping, h=yR/5. Find y.

G1 Physics · Accepted Answer

Step 1: Horizontal linear impulse J gives ball centre speed v=J/M. Step 2: Angular impulse about centre is Jh=Iω; for a solid sphere I=(2/5)MR², so ω=5Jh/(2MR²). Step 3: For instantaneous rolling v=ωR ⇒ J/M=5Jh/(2MR). Step 4: Cancel J/M: 1=5h/(2R)⇒h=2R/5, so y=2.