Two particles of masses 9kg and 18 kg are placed on a smooth horizontal table. A string, which joins them, hangs over the edge supporting a light pulley, which carries a mass 16 kg. The two parts of the string on the table are parallel and perpendicular to the edge of the table. The parts of the string outside the table are vertical. Find the acceleration (in $m / s^{2}$ ) of the particle of mass 16kg. $[take g = 10 m / s^{2}]$

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Detailed Solution

Let T be the tension in the string; a be the acceleration of the mass 18 kg; 2a be the acceleration of mass 9 kg.T = 18a

The mass 16 kg will come down with an acceleration
$a' = \frac{a + 2 a}{2} = \frac{3 a}{2}$

$16 g - 2 T = 16 (\frac{3 a}{2})$

$\Rightarrow 16 g - 4 \times 9 a = 16 (\frac{3 a}{2})$

$\Rightarrow a = \frac{8}{3} m / s^{2}$
$∴$ the acceleration of 16 kg mass $= \frac{3}{2} a = 4 m / s^{2}$

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