Question

In the arrangement shown, the mass $m$ will ascend with an acceleration (Pulley and rope are massless):

• A. Zero
• B. $\frac{g}{2}$
• C. $g$
• D. $2g$

Answer 1

The correct option is B $\frac{g}{2}$

$\text{Step 1: Drawing free body diagram}$ $\text{[Ref. Fig. 1 \& 2]}$

Assuming accelerations of blocks and Tension in the string as shown in the figure

$\text{Step 2: Applying Newton's Third Law at point of application of force F on string}$

We see that F and T are Action-Reaction pairs.

$\therefore T=F=\frac{3}{2}mg$ $....\left(1\right)$

$\text{Step 3: Applying Newton's Second Law on block}$

(Taking positive upwards)

$\sum F_y=ma$

$\Rightarrow$ $T-mg=ma$

From equation $\left(1\right)$

$\Rightarrow \frac{3}{2}mg-mg=ma$

$\Rightarrow$ $a=\frac{g}{2}$

Hence mass $m$ will ascend with an acceleration $a=g/2$

Therefore, Option B is correct