First slide

Connected bodies

Question

A constant force F = m₂g/2 is applied on the block of mass m₁ as shown. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of m₁.

Moderate

A

$\frac{{{m_2}g}}{{2{m_1}}}$
B

$\frac{{{m_2}g}}{{2\left( {{m_1} + {m_2}} \right)}}$
C

$\frac{{3\,{m_2}g}}{{2\left( {{m_1} + {m_2}} \right)}}$
D

$\frac{{3\,{m_2}g}}{{2\,{m_1}}}$

Solution

$T - F = {m_1}a.........(1)$
${m_2}g - T = {m_2}a.........(2)$
(1) + (2)
m₂g – F = (m₁ + m₂)a
${m_2}g - {m_2}\frac{g}{2} = ({m_1} + {m_2})a$
$\Rightarrow \frac{{{m_2}g}}{2} = ({m_1} + {m_2})a$
$\therefore \,\,a = \frac{{{m_2}g}}{{2({m_1} + {m_2})}}$

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