The two spheres are rigidly connected to the rod of negligible mass and are initially at rest on the smooth horizontal surface. A force F is suddenly applied to one sphere in the y-direction and imparts an impulse of 9.8 N·s during a negligibly short period of time. As the spheres pass the dashed position, calculate the magnitude of the velocity of each one.

Complete Question

The complete question is shown on the first uploaded image

The velocity of the both spheres is

Explanation:

The free body diagram of this question is shown on the second uploaded image

     Looking at this diagram we can deduce that there is no impulse force along the horizontal direction so

      The mathematical equation for the impulse force along the horizontal axis is  

 The mathematical equation for the impulse force along the horizontal axis is

  Where is the impulse  momentum along the y-axis and this is mathematically given as

substituting 9.8 N.s for and 1.5kg for m (mass of sphere) and the making the subject

The sum of the moment about the point I is mathematically represented as

From the free body diagram  

is the angular momentum along the horizontal axis  given as

substituting parameters into above equation

Making the subject

the velocity of the sphere is mathematically represented as

Now substituting values

your answer is, orbit around the nucleus