A particle is suspended from O by a string of length L. A vertical line AB is at horizontal distance L/8 from O. The particle is given horizontal speed u. Its circular motion later ceases, and when it crosses AB its velocity is horizontal. Find u.

Question

G1 Physics · Accepted Answer

Let the string go slack when tension first becomes zero. Use radial force balance T=0 together with energy from the bottom to determine the release point and speed; then use projectile motion so that the particle crosses the vertical line x=L/8 with horizontal velocity. Eliminating the release angle gives u=√{gL[2+3√3/2]}.