Question

In the system shown in the figure $m_1>m_2$. System is held at rest by thread $BC$. Just after the thread $BC$ is cut:

(A) Acceleration of $m_2$ will be upwards
(B) Magnitude of acceleration of both blocks will be equal to $\left(\frac{m_1-m_2}{m_1+m_2}\right)g$
(C) Acceleration of $m_1$ will be equal to zero
(D) Magnitude of acceleration of two blocks will be non-zero and unequal.
From the above four statements we can conclude

• A. $\text{Only statement (A) is correct}$
• B. $\text{Only statement (B) is correct}$
• C. $\text{Only statement (C) is correct}$
• D. $\text{Both statement (A) and (C) are correct}$

Answer 1

The correct option is D $\text{Both statement (A) and (C) are correct}$

Before cut, from the FBD of $m_1$ we get
$m_{1}g=kx$

After cut from the FBDs of both the blocks we get,
For block $B$:
$a=\frac{kx-m_{2}g}{m_2}=\frac{m_{1}g-m_{2}g}{m_2}$
$\because$ the mass of $m_1$ is greater than $m_2$, the block will have acceleration upwards.
For block $A$:
$a=\frac{m_{1}g-kx}{m_1}=0$