Question

The system of figure 1 is released from rest. In the figure, $2$ the block of m is pulled with force $2mg$. If the acceleration are $a_1$ and $a_2$ in figure $1$ and $2$ respectively then

• A. $a_1=\frac{2g}{3}$
• B. $a_1=g$
• C. $a_2=2g$
• D. $a_2=\frac{g}{3}$

Answer 1

The correct option is A $a_1=\frac{2g}{3}$

$F=ma$

$F=(m_1+m_2)a$

$a=\frac{F}{m_1+m_2}⟶\left(1\right)$

$N_{21}$ is making $n_2$ accelerate

$N_{21}=$

In $1st$ case,

$Ma=2mg-mg$

$a=g$

In $2nd$ case,

$T-mg={ma}^{{}^{\prime }}$

$2mg-T={2ma}^{{}^{\prime }}$

$a^{{}^{\prime }}=\frac{g}{3}$

$a-a^{{}^{\prime }}=\frac{2g}{3}$.