Question

Two block of mass $m_A=10\text{kg}$ and $m_B=15\text{kg}$ are connected by a light inextensible string and placed on a smooth horizontal surface as shown in the figure. Find the value of tension force on block $A$, if force applied on block $B$ is $50\sqrt{3}\text{N}$ .

• A. $30\text{N}$
• B. $45\text{N}$
• C. $15\text{N}$
• D. $75\text{N}$

Answer 1

The correct option is A $30\text{N}$

$\Rightarrow$The forces in vertical direction are balanced for both bodies, because system will be moving only in horizontal direction.

From the FBD of blocks:

For block $A$
$T=m_{A}a=10a...\left(i\right)$
For block $B$
$F\cos \theta -T=m_{B}a=15a...\left(ii\right)$
Adding equation $\left(i\right)$ and $\left(ii\right)$:
$F\cos \theta =25a$
$75=25a$
$\therefore a=\frac{75}{25}=3{\text{m/s}}^2$
$\Rightarrow T=m_{A}a=10\times 3=30\text{N}$