Question

The blocks of masses $4\text{kg, 6 kg and 8 kg}$ are hanging over a fixed pulley as shown. The tension in the string connecting $8\text{kg and 4 kg}$ block is

• A. 4 N
• B. 6 N
• C. $\begin{array}{cc}& \frac{160}{3}\text{N}\\ & \end{array}$
• D. $\begin{array}{cc}& \frac{80}{3}\text{N}\\ & \end{array}$

Answer 1

The correct option is D $\begin{array}{cc}& \frac{80}{3}\text{N}\\ & \end{array}$

Let teh tension in the section of string between 6 kg and 8 kg mass be $T_1$ and tenstion between the 8 kg and 4 kg mass be $T_2$

Assuming ace;eration of systm as a we have for :

(i) 6 kg mass $\to T_1-6g=6a\to \left(1\right)$

(ii) 8 kg mass $\to T_2+8g-T_1=8a\to \left(2\right)$

(iii) 4 kg mass $\to 4g-T_2=4a\to \left(3\right)$

from equation (3) $T_2=4g-4a\to \left(4\right)$, substituting in equation (2) we get :

$12g-4a-T_1=8a\Rightarrow T_1=12g-12a$

Substituting this value in equation (1) we get :

$6g-12a=6a\Rightarrow 18a=6g$

$\Rightarrow a=\frac{g}{3}$

Hence equation (4) becomes :

$T_2=4g-\frac{4g}{3}=\frac{8g}{3}=\frac{80}{3}N$