Question

Please answer this question for me and explain why.

Answer 1

Answer:

D.None of these

Explanation:

The derivation of acceleration formula:

Let us call the 5kg mass $m_2$ and the 4kg mass $m_1$. If the tension in the string is $T$ then for the mass $m_2$

(1). $T-m_2g=-m_2a$ (the negative sign on the right side indicates that acceleration is downwards)

And for the mass $m_1$

(2). $T-m_1g =m_1a$ (the acceleration is upwards, hence the positive sign)

Solving for $T$ in the 2nd equation we get:

$T =m_1a+m_1g$,

and putting this into the 1st equation we get:

$m_1a+m_1g-m_2g=-m_2a\\\\m_1a+m_2a = m_2g-m_1g\\\\a(m_1+m_2)= (m_2-m_1)g$

$\boxed{a= \dfrac{(m_2-m_1)}{(m_1+m_2)} g}$

Back to the question:

Using the formula for the acceleration we find

$a= \dfrac{(5kg-4kg)}{(5kg+4kg)} g$

$a = \dfrac{g}{9},$

which is the acceleration that none of the given choices offer. Also, the acceleration of the two blocks is the same, because if it weren't, the difference in the instantaneous velocities of the objects would cause the string to break. Therefore, these two reasons make us decide that none of the choices are correct.