First slide

Connected bodies

Question

If masses are released from the position shown in figure then time elapsed before mass m₁ collides with the floor will be :

Moderate

A

$\large \sqrt {\frac{{2{m_1}gd}}{{{m_1} + {m_2}}}}$
B

$\large \sqrt {\frac{{2({m_1} + {m_2})d}}{{({m_1} - {m_2})g}}}$
C

$\large \sqrt {\frac{{2({m_1} - {m_2})d}}{{({m_1} + {m_2})g}}}$
D

None of these

Solution

$\large d = \frac{1}{2}a{t^2};$ $a = (\frac{m_1-m_2}{m_1+m_2})g$
$\Rightarrow t=\sqrt{\frac{2d(m_1+m_2)}{(m_1-m_2)}}$

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