Question

Two blocks of masses $2.9\text{kg}$ and $1.9\text{kg}$ are suspended from a rigid support by two inextensible wires each of length $1\text{m}$, the upper wire has negligible mass and the lower wire has a uniform mass of $0.2\text{kg/m}$. The whole system of block, wire and support has an upward acceleration of $0.2{\text{m/s}}^2$.
The tension at the mid-point of lower wire is:

• A. $10.4\text{N}$
• B. $20.4\text{N}$
• C. $20\text{N}$
• D. $30\text{N}$

Answer 1

The correct option is C $20\text{N}$

Total mass of lower wire, $m_w=0.2\times 1=0.2kg$
Since the wire is uniform, therefore mass of the half wire length will also be half i.e. $0.1kg$
Considering FBD consisting of half of lower wire and lower block,
Using Newton's second law,
$T-2g=2\left(0.2\right)$
$\Rightarrow T=19.6+0.4=20\text{N}$