Question

Three blocks $A$,$B$ and $C$ weighing $1,8$ and $27\text{kg}$ respectively are connected as shown in the figure with an inextensible string and are moving on a smooth surface. If $T_3$ is equal to $36\text{N}$, then $T_2$ is

• A. $18\text{N}$
• B. $9\text{N}$
• C. $3.375\text{N}$
• D. $1.25\text{N}$

Answer 1

The correct option is B $9\text{N}$

Block $A,B$ and $C$ are tied with an inextensible string
$\therefore$ Acceleration $\left(a\right)$ will be same for all

$(m_A+m_B+m_C)\times a=T_3$
$\Rightarrow a=\frac{T_3}{(m_A+m_B+m_C)}=\frac{36\text{N}}{36\text{kg}}=1{\text{m/s}}^2$


From FBD of $1\text{kg}$ body,
$m_A\times a=T_1$
$1\times 1=T_1$
$T_1=1\text{N}$


Again, from FBD of $8\text{kg}$ body, we get
$T_2-T_1=m_{B}a$
$T_2=T_1+m_{B}a$
$T_2=1+8\times 1=9\text{N}$