Question

In the figure shown, the tension at the mid – point of the rope of mass $3\text{kg}$ (point $B$) is $13\text{N}$. Find the tension in the rope at point $C$.

• A. $10\text{N}$
• B. $16\text{N}$
• C. $20\text{N}$
• D. $25\text{N}$

Answer 1

The correct option is B $16\text{N}$

Let the tension at the mid-point $B$ of the rope be $T_B$
So, the acceleration of the system can be calculated as

From the above FBD we have
$T_B=(5+1.5)a$
$13=6.5a$ (As given $T_B=13N$)
$\Rightarrow a=2{\text{m/s}}^2$

Now, consider the FBD of the entire system as shown

So, the force applied is given by
$F=\text{Mass}\times a=10\times 2=20\text{N}$

Let the tension at point $C$ be $T_C$


From FBD of $2\text{kg}$ body we have
$F-T_C=2a$
$\Rightarrow T_C=20-2\left(2\right)$
$=16\text{N}$

Alternate:
Consider the above situation as shown


From the FBD shown above we have,
$T_C=8a=8\times 2=16N$