Motion Of Blocks When Connected With String - Practice Questions & MCQ

1. Two blocks connected with a string on smooth horizontal surface

Let accelereration of the blocks be 'a', and Tension in the string be T.

F.B.D of both blocks combined-

$
\begin{aligned}
& \text { From } F_{n e t}=M_{s y s} a \\
& F=\left(m_1+m_2\right) a \\
& \Rightarrow a=\frac{F}{m_1+m_2} \ldots
\end{aligned}
$

F.B.D of block of mass m₁-

$\begin{aligned} & \text { From } F_{\text {net }}=M_{\text {sys }} a \\ & T=m_1 a \\ & \text { From equation }(1) \\ & \Rightarrow T=\frac{m_1 F}{m_1+m_2} \ldots(2)\end{aligned}$

2. Three blocks connected with a string on smooth horizontal surface

Let accelereration of the blocks be 'a', tension in the string between m₁ and m₂ be T₁, and tension between m₂ and m₃ be T₂.

F.B.D of all the blocks combined-

$
\begin{aligned}
& \text { From } F_{\text {net }}=M_{\text {sys }} a \\
& F=\left(m_1+m_2+m_3\right) a \\
& \Rightarrow a=\frac{F}{m_1+m_2+m_3} \ldots
\end{aligned}
$

F.B.D of block m_1-

_{From $F_{\text {net }}=M_{\text {sys }} a$
$T_1=m_1 a$
From equation (1) -}

_{$
\Rightarrow T_1=\frac{m_1 F}{m_1+m_2+m_3} \ldots
$}
 

F.B.D of m_3-

$
\begin{aligned}
& \text { From } F_{\text {net }}=M_{\text {sys }} a \\
& F-T_2=m_3 a \\
& \Rightarrow T_2=\frac{\left(m_1+m_2\right) F}{m_1+m_2+m_3} \ldots
\end{aligned}
$