Question

If the acceleration of the elevator is $a_0=g$, then

• A. The acceleration of the masses will be $a_0$
• B. The acceleration of the masses will be $(a_0+g)$
• C. The tension in the string will be $\frac{Mm}{M+m}(g+a_0)$
• D. Tension in the string will be zero.

Answer 1

The correct option is D Tension in the string will be zero.

Using the concept of pseudo force in the frame of elevator we have,
FBDs of both the blocks are as shown

Let acceleration of the masses w.r.t pulley be $a$.
For $M:$ $Mg-T-M{a}_0=Ma$;
Foro $m:$ $T+m{a}_0-mg=ma$;
$\Rightarrow a=\frac{M-m}{M+m}(g-a_0)\Rightarrow T=\frac{2Mm}{M+m}(g-a_0)$
$\because$ $a_0=g$
$\Rightarrow a=0\text{and}T=0$