Question

Three blocks of mass $2kg$, $3kg$ and $5kg$ are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force of $10\text{N}$, tension $T_1$ is equal to

• A. $1N$
• B. $5N$
• C. $8N$
• D. $10N$

Answer 1

The correct option is C $8N$

FBD of the system


Writing the force equations,
$10-T_1=2a$
$T_1-T_2=3a$
$T_2=5a$

(aceleration $a$ is common for the system because the strings can’t stretch or become slack)

Solving the equations, we get
$T_1=8N$

Alternate method :
Common acceleration $a=\frac{\text{Net external force}}{\text{Total mass}}=\frac{10}{10}=1m/s^2$

Considering the $3kg$ and $5kg$ blocks as a system, $T_1$ is the external force responsible for moving the system.

Hence, $T_1=a(3+5)=8a=8N$