What is the acceleration of block B for the g | vedclass

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(A) Let the acceleration of block $B$ be $a$. Due to the movable pulley,the acceleration of block $A$ will be $2a$.For block $A$ (mass $m_1$): The ten

Vedclass · Accepted Answer

$\frac{{{m_2}g}}{{(4{m_1} + {m_2})}}$

Vedclass · Answer

(A) Let the acceleration of block $B$ be $a$. Due to the movable pulley,the acceleration of block $A$ will be $2a$.For block $A$ (mass $m_1$): The tension $T$ acts as the net force. $T = m_1(2a) = 2m_1a$ .....$(i)$For block $B$ (mass $m_2$): The forces acting are gravity $m_2g$ downwards and tension $2T$ upwards. $m_2g - 2T = m_2a$ .....(ii)Substitute $T = 2m_1a$ from equation $(i)$ into equation (ii):$m_2g - 2(2m_1a) = m_2a$$m_2g - 4m_1a = m_2a$$m_2g = m_2a + 4m_1a$$m_2g = a(m_2 + 4m_1)$$a = \frac{m_2g}{4m_1 + m_2}$

What is the acceleration of block $B$ for the given system?

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