Question

two stationary objects of mass 1 kg and 2 kg are connected by a thread and suspended from a spring. the thread is cut. immediately after the cut, what are the magnitudes of the accelerations of the objects in terms of the acceleration due to gravity ( g )?

	acceleration of 1kg object	acceleration of 2kg object
b	( 2g )	( 2g )
c	( 3g )	( 1g )
d	( 2g )	( 1g )

diagram: spring attached to a fixed support, 1kg mass hanging from the spring, thread connecting the 1kg mass to a 2kg mass below

Explanation:

Step1: Analyze forces before cutting the thread

Before cutting the thread, the system is in equilibrium. Let the spring force be \( F_s \). The total mass is \( m_{total}=1\,\text{kg} + 2\,\text{kg}=3\,\text{kg} \). So, \( F_s = m_{total}g=3g \) (since the net force on the system is zero, spring force balances the total weight).

Step2: Analyze 1 kg object after cutting the thread

After cutting the thread, the forces on the 1 kg object are the spring force \( F_s = 3g \) upward and its weight \( mg = 1g \) downward. Using Newton's second law \( F = ma \), for the 1 kg object:
\( F_s - m_1g=m_1a_1 \)
Substitute \( F_s = 3g \) and \( m_1 = 1\,\text{kg} \):
\( 3g - g=1\times a_1 \)
\( 2g=a_1 \)

Step3: Analyze 2 kg object after cutting the thread

After cutting the thread, the only force on the 2 kg object is its weight (since the thread is cut, tension disappears). Using Newton's second law \( F = ma \), for the 2 kg object:
\( m_2g=m_2a_2 \)
Cancel \( m_2 \) ( \( m_2 = 2\,\text{kg}
eq0 \) ):
\( a_2 = g \)

Answer:

The acceleration of the 1 kg object is \( 2g \) and the acceleration of the 2 kg object is \( g \), so the correct option is D. D. Acceleration of 1kg object: \( 2g \), Acceleration of 2kg object: \( g \)