Question

For the system shown in the figure, the pulley is smooth and massless, the string is massless and inextensible. If the acceleration of the system is ($a$) then, find out the ratio of tensions $T_1$ and $T_2$.
(Take $g=10{\text{m/s}}^2)$

• A. $20:3$
  
• B. $5:1$
  
• C. $3:1$
  
• D. $5:2$
  

Answer 1

The correct option is C $3:1$


Here, net pulling force will be
(weight of $4\text{kg}$ and $2\text{kg}$ blocks on one side)$-$ (weight of $4\text{kg}$ block on the other side ).
Acceleration of the system is given by $a$;
$\therefore a=\frac{\text{Net pulling force}}{\text{Total mass}}$

$\Rightarrow a=\frac{(2\times 10)+(4\times 10)-(4\times 10)}{2+4+4}$

$\therefore a=\frac{20}{10}=2{\text{m/s}}^2$

For $T_1$:
From FBD of $4\text{kg}$ block,
$T_1-40=4a$
$T_1=40+4a$
$T_1=40+(4\times 2)=48\text{N}$

For $T_2$:
From FBD of $2\text{kg}$ block,

$mg-T_2=2a$
$\Rightarrow T_2=20-2a$
$\therefore T_2=20-2\times 2=16\text{N}$

$\Rightarrow \frac{T_1}{T_2}=\left(\frac{48}{16}\right)=3:1$