Question

In the figure shown, find the tension at the midpoint of the rope of mass $2\text{kg}$ connecting the masses $3\text{kg}$ and $5\text{kg}$. Given $F=30N$.

• A. $10\text{N}$
• B. $11\text{N}$
• C. $12\text{N}$
• D. $15\text{N}$

Answer 1

The correct option is C $12\text{N}$

Consider both the blocks and the rope as a system .
Hence, acceleraton of the system =
$a=\frac{\text{Force}}{\text{Total mass}}=\frac{30}{10}=3{\text{m/s}}^2$
To find the tension at the mid-point of the rope, we need to consider the force acting on the total mass to the left of the mid-point

$T=(3+1)a$
$=4\times 3=12\text{N}$