Question

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:

• A. $\frac{4ab}{(a+b)}$
  
• B. $\frac{3ab}{(a+b)}$
• C. $\frac{2ab}{(a+b)}$
• D. $\frac{ab}{(a+b)}$

Answer 1

Answer: (A)

$\frac{4ab}{(a+b)}$


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 $T=4ab/(a+b)$