A heavy object having mass $m _ { a }$ is attached to a massless cord. The cord is wrapped around a massless pulley, and the other end of the cord is attached to a lighter object having mass $m _ { b } \left( m _ { a } m _ { b } \right)$. The two masses are released. Find the acceleration of the masses.
A) $2 g m _ { b } / \left( m _ { a } + 2 m _ { b } \right)$
B) $2 g m _ { a } / \left( m _ { a } + m _ { b } \right)$
C) $g \times \left( m _ { b } - m _ { a } \right) / \left( 2 m _ { a } + m _ { b } \right)$
D) $g \times \left( m _ { a } - m _ { b } \right) / \left( m _ { a } + m _ { b } \right)$

Question

A heavy object having mass $m _ { a }$ is attached to a massless cord. The cord is wrapped around a massless pulley, and the other end of the cord is attached to a lighter object having mass $m _ { b } \left( m _ { a } > m _ { b } \right)$. The two masses are released. Find the acceleration of the masses.
A) $2 g m _ { b } / \left( m _ { a } + 2 m _ { b } \right)$
B) $2 g m _ { a } / \left( m _ { a } + m _ { b } \right)$
C) $g \times \left( m _ { b } - m _ { a } \right) / \left( 2 m _ { a } + m _ { b } \right)$
D) $g \times \left( m _ { a } - m _ { b } \right) / \left( m _ { a } + m _ { b } \right)$

Quizplus · Accepted Answer

The acceleration of the system can be found using Newton's second law. The net force on the system is the difference in the gravitational forces acting on the two masses, $m_a g - m_b g$, and the total mass of the system is $m_a + m_b$. Thus, the acceleration $a$ is given by $a = \frac{m_a g - m_b g}{m_a + m_b} = g \times \frac{m_a - m_b}{m_a + m_b}$.

A Heavy Object Having Mass mam _ { a }ma​ Is Attached to a Massless Cord

A Heavy Object Having Mass $m _ { a }$ Is Attached to a Massless Cord