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Two masses of...

Question

Two masses of $8 k g$ and $4 k g$ are connected by an unstretchable and massless string as shown in the figure over a frictionless pulley. The acceleration of the two block system is:

4 {m / s}^{2}

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2 {m / s}^{2}

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0

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9.8 {m / s}^{2}

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Solution

The correct option is C $0$
FBD is shown above.
For block $m_{2}$ ,
Equation of motion is $m_{2} a = m_{2} g - T$ ,
We get $T = m_{2} (g - a)$
For block $m_{1}$ ,
$m_{1} a = T - m_{1} g sin 30$
$∴ m_{1} a = m_{2} (g - a) - m_{1} g sin 30$
$∴ a = \frac{(m_{2} - m_{1} sin 30) g}{m_{1} + m_{2}}$
Given : $m_{1} = 8 k g$ $m_{2} = 4 k g$
Thus, $a = \frac{4 - (8) (0.5)}{8 + 4} = \frac{4 - 4}{12} = 0$

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Two masses of 8kg and 4kg are connected by an unstretchable and massless string as shown in the figure over a frictionless pulley. The acceleration of the two block system is:

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