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Q.

Two bodies of masses $15 k g$ and $5 k g$ are connected to the ends of a mass less cord and allowed to move as shown in figure. The pulley is massless and friction less. Calculate the acceleration of the centre of mass:-

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a

$- 5 m / s^{2}$

b

$5 m / s^{2}$

c

$- \frac{5}{2} m / s^{2}$

d

$\frac{5}{2} m / s^{2}$

answer is D.

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Detailed Solution

$\begin{aligned} a_{cm} = \frac{m_{1} {\vec{a}}_{1} + m_{2} {\vec{a}}_{2}}{m_{1} + m_{2}} \\ a_{1} = (\frac{15 - 5}{15 + 5}) g = \frac{g}{2}, {\vec{a}}_{1} = - \frac{g}{2} \hat{j}, {\vec{a}}_{2} = \frac{g}{2} \hat{j} \\ a_{cm} = \frac{\frac{1}{2} (- 15 + 5) g}{20} = \frac{- 10}{4} = \frac{- 5}{2} m / s^{2} \end{aligned}$

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Two bodies of masses 15 kg and 5 kg are connected to the ends of a mass less cord and allowed to move as shown in figure. The pulley is massless and friction less. Calculate the acceleration of the centre of mass:-