Question

In the figure, pulleys are smooth and strings are massless $m_1=1kg$ and $m_2=\frac{1}{3}kg$. To keep $m_3$ at rest, $m_3$ should be

• A. $1kg$
• B. $\frac{1}{2}kg$
• C. $\frac{4}{3}kg$
• D. $2kg$

Answer 1

The correct option is A $1kg$

$\left(1\right)\Rightarrow 3T_1-g=a\to \left(5\right)\left(4\right)\Rightarrow g-T_1=a\left(5\right)=\left(4\right)\Rightarrow 3T_1-g=g-T_1\Rightarrow T_1=\frac{g}{2}\left(2\right)\Rightarrow T_2=2T_1\Rightarrow T_2=2\times \frac{g}{2}{T}_2=g\to \left(6\right)\left(7\right)in\left(3\right)\Rightarrow g=m_{3}g\Rightarrow m_3=1㎏$