Question

Three masses of $1kg,6kg$ and $3kg$ are connected to each other with strings and are placed on a table as shown in figure. What is the acceleration with which the system is moving? (Take $g=10m{s}^{-2}$ )

• A. $zero$
• B. $1m{s}^{-2}$
• C. $2m{s}^{-2}$
• D. $3m{s}^{-2}$

Answer 1

Answer: (C)

Here, $m_1=1kg,m_2=6kg$ and $m_3=3kg$
Let $a$ be the acceleration with which the system is moving. The equations of motion of three masses are
$m_{1}a=T_1-m_{1}g$
$m_{2}a=T_2-T_1$
$m_{3}a=m_{3}g-T_2$
Adding $(i),(ii)$ and $(iii)$, we get
$a\left(m_1+m_2+m_2\right)=\left(m_3-m_1\right)g$
$\therefore a=\frac{\left(m_3-m_1\right)g}{\left(m_1+m_2+m_3\right)}=\frac{(3-1)\times 10}{1+6+3}=2m{s}^{-2}$