$1)$Two spheres A and B are placed in the arrangement shown below.

$($a$)$ If $m_A=3m$ and $m_B=6m,$ where on the dashed line should a third sphere $C$ of mass $6m$ be placed so that the net force on it is zero?

to the right of $A$

at the midpoint between A and $B$

between A and $B,$ closer to $A$

to the left of $B$

between A and $B,$ closer to $B$

$($b$)$ If the distance between the two spheres A and B is $500cm,$ find the location for the third sphere C so that the net force on it is zero.

$Cm$ to the right of sphere $B$