Question

Three equal weights $A,B$ & $C$ each of mass $2\text{kg}$ are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in string connecting $B$ and $C$ approximately is

• A. Zero
• B. $13\text{N}$
• C. $3.3\text{N}$
• D. $19.6\text{N}$

Answer 1

The correct option is B $13\text{N}$

Let the acceleration of the mass A be $2a$ in upward direction.
For mass $C$, resultant force on $C=2g-T_2$

$\therefore 2g-T_2=2a$ ... (1)
For mass $B,2g+T_2-T_1=2a$ ... (2)
For mass $A,T_1-2g=2a$ ... (3)
Adding $\left(1\right)$, $\left(2\right)$ and $\left(3\right)$,
$a=\frac{2g}{6}=\frac{g}{3}$
Tension, $T_2=2g-2a=2g-\frac{2g}{3}$
$=\frac{4g}{3}=\frac{4\times 9.8}{3}=\frac{39.2}{3}=13\text{N}$
$\therefore$ (B)