Two weights $a$ and $b$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration $g$, then the tension in the string will be:

The correct option is C $\frac{4ab}{(a+b)}$

Let acceleration of $a$ and $b$ be $a-a$ and $a_b$ considering$b$ to be moving downward and a to be moving upwards.
Clearly $a_a+g=a_b-g$
Equation of motion of $a$ and $b$ will be,
$T-ag=a(a_a+g)$
$T-bg=b(g-a_b)$
Solving above eqns,
We get $T=4ab/(a+b)$