Motion Of Connected Blocks Over Pulley - Practice Questions & MCQ

Equation of motion for $m_1$

$
F_{n e t}=T-m_1 g=m_1 a
$

Equation of Motion for $m_2$

$
\begin{aligned}
& F_{\text {net }}=m_2 g-T=m_2 a \\
& a=\frac{\left[m_2-m_1\right] g}{m_1+m_2} \\
& T=\frac{2 m_1 m_2 g}{m_1+m_2}
\end{aligned}
$
 

1. When one Block is hanging, other is on the Table

     $\begin{aligned} a & =\frac{m_2 g}{m_1+m_2} \\ T & =\frac{m_1 m_2 g}{m_1+m_2}\end{aligned}$

2. Three blocks, two are hanging and one is at the rest on the smooth horizontal table

$
\begin{aligned}
& m_1 a=m_1 g-T_1 \\
& m_2 a=T_2-m_2 g \\
& T_1-T_2=M a
\end{aligned}
$

$
\begin{aligned}
& a=\frac{\left(m_1-m_2\right) g}{m_1+m_2+M} \\
& T_1=\frac{m_1\left(2 m_2+M\right) g}{\left(m_1+m_2+M\right)} \\
& T_2=\frac{m_2\left(2 m_1+M\right) g}{\left(m_1+m_2+M\right)}
\end{aligned}
$