let mass of ball be m

using conservation of momemtum::mv = MV

=> V = mv/M ---->(1)


conserving angular momentum:: mv L/2 = I w where I is moment of inertia of rod & w is angular velocity of rod after collision

=> mvL/2 = ML^2 /12 * w

=>w = 6mv/ML ----(2)

since, collision is elastic,
therefore, using conservation of energy
1/2 m v^2 = 1/2MV^2 + 1/2 I w^2

=> m v^2 = MV^2 + (ML^2)/12 w^2

putting the values from (1) & (2) & solving

 

mv^2 = (m^2 v^2)/M + 3 (m^2 v^2)/M

 

=> m = 4 (m^2)/M

 

=>m = M/4  (ans.)

 

i guess this should be correct....