Question

In the figure shown, all the blocks are of equal mass of $10\text{kg}$ and $F=300\text{N}$. Find the tension in the string, $T_{BC}$. Assume all surface to be smooth and $g=10{\text{m/s}}^2$.

• A. $100\text{N}$
• B. $150\text{N}$
• C. $200\text{N}$
• D. $250\text{N}$

Answer 1

The correct option is C $200\text{N}$

Considering all the blocks to be a single system ie. $(10+10+10=30kg)$, FBD of the system will be

$F-30g\sin 30°=30a$
$\Rightarrow 300-150=30a$
$\Rightarrow a=5{\text{m/s}}^2$
Hence whole system will be accelerating upwards at $5{\text{m/s}}^2$
Considering FBD of system combining blocks A and B,

$T_{BC}-20g\sin 30°=20a$
$\Rightarrow T_{BC}=20\left(5\right)+100$
$T_{BC}=200\text{N}$