Question

Find the tension in the string connected to the block of mass $4\text{kg}$. Assume the strings and pulleys to be ideal. (Take $g=10m/s^2)$

• A. $\frac{100}{9}N$
• B. $\frac{40}{3}N$
• C. $\frac{15}{2}N$
• D. $\frac{50}{3}N$

Answer 1

The correct option is B $\frac{40}{3}N$

The given system can be reframed as shown

From constraint condition, we have
(i) ${\stackrel{..}{L}}_1+{\stackrel{..}{L}}_2=0\Rightarrow -a_2+a_p=0\Rightarrow a_p=a_2$
(ii) ${\stackrel{..}{L}}_3+{\stackrel{..}{L}}_4=0\Rightarrow -a_p-a_p+a_1=0\Rightarrow a_1=2a_p$
Hence, $a_1=2a_2$

Hence, let acceleration of $2kg$ block is $a$ upwards, and acceleration of $4kg$ block is $2a$ downwards.

Applying Newton's Second Law,

For $2\text{kg}$ body:
$2T-20=2a$ ... (3)

For $4\text{kg}$ body:
$40-T=4\times 2a$ ... (4)
From (3) and (4)
$4\times (2T-20)=40-T$
$\Rightarrow 9T=120\Rightarrow T=\frac{120}{9}$
Thus, the tension in the string connecting $4kg$ mass is $T=\frac{120}{9}=\frac{40}{3}N$