Question

A particle of mass m starts at rest on top of a smooth fixed hemisphere of radius R. Find the force of constant, and determine the angle at which the particle leaves the hemisphere.

Answer 1

Uso h = R-Rloso h = RCI-Coso) ------ RCase Let's consider a hemisphere of Radices 'R' we assume that the object leaves the hemisphere at point B. Now we will discuss the free body diagram of the object at B' ON 2 4--- - mgcoso 1 Net force = my² mg sino R mg coso -N = my? S het vis the velocity at point B But at this paint the object leves the surface of hemisphere so the Reaction force at this point becomes zero. Hence force of contact [N=0] so the equation becomes mgloso = mur v² = gR coso - ci Applying energy conservation between A & B. EA = EB → mgh I mv² JRC1-Coso) - v? v² = 2GR (1-coso) - (ii) R

Equating equation () { (ii) GR Coso = 28 RC1-Coso) Coso = 2-2 coso 3 Coso = 2 Coso = 2 2 0 = cost { 2 } So the angle at which the object 0 = 46.19° leaves the hemisphere is 48-190
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