Question

Find the ratio of tensions $T_1$ to $T_2$ for the figure shown.

• A. $8:5$
• B. $5:8$
• C. $3:4$
• D. $4:3$

Answer 1

The correct option is A $8:5$

The acceleration, $a$ of the system will be in downward direction for hanging masses.
As $T_1$ is the tension due to the mass $(3\text{Kg}+5\text{Kg})$ so, considering $8\text{kg}$ as effective mass, we can draw its free body diagram as
$8g-T_1=8a$
$⟹T_1=8(g-a)$
Now, $T_2$ is the tension due to the $5\text{Kg}$ mass so,

$5g-T_2=5a⟹T_2=5(g-a)$
$\therefore$ $\frac{T_1}{T_2}=\frac{8}{5}$
Alternate solution:
Let us consider all the four blocks to form a system.
Here, effective force acting on the system is in the downward direction (i.e. $(5+3+2)g=10g$)
$\therefore \text{acceleration}=\frac{Effectiveforce}{Totalmass}=\frac{10g}{20}=5m/s^2$
Now, for $5kg$ block, we can write
$5g-T_2=5a$
$⟹T_2=25N$
For $3kg$ block, we can write
$3g+T_2-T_1=3a$
$⟹T_1=40N$
Hence, $T_1:T_2=40:25=8:5$