Let vo is the initial speed of clay.
let w is the angular speed of rod just after the collision,
Moment of Inertia of rod = M*L^2/12
= 10*m*L^2/12
mment of inertia about pivot = m*L^2
vertical vertical displacement of the center of mass of rod
= L/2
vertical dispalcement of clay = L
after the collsion apply conservation of
energy
final potentail energy = initial kinetic energy
m*g*L + M*g*(L/2) = 0.5*I*w^2
m*g*L + 10*m*g*(L/2) = 0.5*(10*m*L^2/12 + m*L^2)*w^2
6*m*g*L = (22/24)*m*L^2*w^2
6*g = (22/24)*L*w^2
w^2 = 6*g*L*24/22
w = sqrt(6*9.8*24/22)
= 8 rad/s <<<<<<<<<-------------------Answer for part B)
when the collsion takes place apply conservation of angular momentum
m*vo*L = I*w
m*vo*L = (10*m*L^2/12 + m*L^2)*w
m*vo*L = (22/12)*m*L^2*w
vo = (22/12)*L*w
vo = (22/12)*L*8
= 14.67*L -------------------Answer for part A)
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