Question

Three blocks 1,2 and 3 are arranged with pulley and spring as shown in the figure. If string connecting blocks $m_2$ and $m_3$ is cut at point A, find the accelerations of masses $m_1$, $m_2$, and $m_3$_­ just after the string is cut at point A.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Before cutting the system was in equilibrium. Nothing moved No acceleration. Let's draw free body diagram and analyze the situation.

$K_x=m_{1}g$ ------------(1)

Now as soon as string is cut at A both the string will slack. Once the string slacks immediately the Tension $T_1$ & $T_2$ will become 0

$\Rightarrow$ lets analyze the new free body diagram of all the block.

$T_1$ & $T_2$ = 0

$\Rightarrow$ $m_3$g = $m_3$$a_3$ so $a_3$ = g ($m_3$ falls under gravity)

$T_2=0$

but $k_x$ is still there

$F_{net}=m_{2}g+kx$ $(\because kx=m_{1}g)$

$F_{net}=(m_1+m_2)g=m_2{a}_2)$

$\Rightarrow a_2=\frac{(m_2+m_1)}{m_2}g$

$a_2=(1+\frac{m_1}{m_2})g$

$F_{net}=m_{1}g-kx=m_1{a}_1$

$(\because kx=m_{1}g)$

$\Rightarrow F_{net}=0=m_1{a}_1$

So $a_1=0$