Question

In the given figure if acceleration of <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $m_1$ is 2 m/$s^2$ upward and acceleration of $m_2$ is 4 m/$s^2$ downwards, then acceleration of $m_3$ is

• A.
  4 m/$s^2$ upwards
• B.
  2 m/$s^2$ upwards
• C.
  1 m/$s^2$ downwards
• D.
  0 m/$s^2$

Answer 1

The correct option is D

0 m/$s^2$
Net work done by the internal forces on the system = 0.
Here $T$ is the tension in the string connecting $m_2$ and $m_3$.
Let $x_1$, $x_2$ and $x_3$ are displacements of $m_1$,$m_2$ and $m_3$ in time t respectively.
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $2T{x}_1-T{x}_2+T{x}_3=0$
After differentiating this equation twice w.r.t. time, we get,
$2T{a}_1-T{a}_2+T{a}_3$ = 0
$\Rightarrow$ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $a_3$ = 0