Question

In the given system all the strings & pulleys are mass less and there is no friction between surfaces.
If $m_1=10kg$, $m_2=4kg$ and $m_3=2kg$, then the acceleration of the system is

• A. $\frac{5g}{2}$
• B. $\frac{5g}{3}$
• C. $\frac{5g}{8}$
• D. $\frac{5g}{14}$

Answer 1

The correct option is C $\frac{5g}{8}$

The equation of motion of the mass $m_1$ is,
$m_{1}a=m_{1}g-T_1$, where a be the acceleration of the system.
$10a=10g-T_1....\left(1\right)$
For mass $m_3$, $m_{3}a=T_2-m_{3}g$
$2a=T_2-2g......\left(2\right)$
For mass $m_2$, $m_{2}a=T_1-T_2+m_{2}gsin30$
$4a=T_1-T_2+4\times \frac{1}{2}g$
$4a=T_1-T_2+2g......\left(3\right)$
Equations $\left(1\right)+\left(2\right)$ $⟹12a=8g-T_1+T_2$
$T_1-T_2=8g-12a$
Now (3) becomes, $4a=8g-12a+2g$
$16a=10g$
$⟹a=\frac{5g}{8}$