Ball a has half the mass and eight times the kinetic energy of ball
b. what is the speed ratio va / vb ?

Explanation :

It is given that there are two balls a and b. Ball a has half the mass of ball b. The kinetic energy of ball a is eight times the kinetic energy of ball b.

We know that the kinetic energy of an object is given by :

Taking ratios of kinetic energy of both balls a and b.

So,

Hence, this is the required solution.                          

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach