Question #42496

A sealed container filled with an ideal incompressible liquid of density $\rho$ accelerates vertically upwards with an acceleration $a = g$. Inside the liquid, two solid spheres A and B, each of volume $V$, collide head-on. The densities of A and B are $\rho_A = \frac{5}{2}\rho$ and $\rho_B = \frac{11}{2}\rho$, respectively. Just before the collision, their relative velocity of approach is $v_0$. Assuming the collision is perfectly elastic and the added mass of a sphere of volume $V$ in this liquid is $\frac{1}{2}\rho V$, find the magnitude of the normal contact impulse exchanged between the two spheres. (Ignore hydrodynamic interactions between the spheres prior to contact, and assume the collision time $\Delta t \to 0$).