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. $T_1$ is equal to $2\text{N}$. Then $T_3$ is

• A. $18\text{N}$
• B. $36\text{N}$
• C. $72\text{N}$
• D. $144\text{N}$

Answer 1

The correct option is C $72\text{N}$

Given $m_A=1kg,m_B=8kg$ and $m_C=27kg$
Let the common acceleration of the system be $a$.

From the FBD of $A$, we have

$T_1=m_A\times a⟹2=1\times a⟹a=2m/s^2$

From the FBD of the whole system, we get

$T_3=(m_A+m_B+m_C)\times a$
$⟹T_3=36a=36\times 2=72N$