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Pulley

If pulley sho...

Question

If pulley shown in the diagram are smooth and massless and $a_{1}$ and $a_{2}$ are acceleration of blocks of mass $4 kg$ and $8 kg$ respectively, then

a_{1} = a_{2}

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a_{1} = 2 a_{2}

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2 a_{1} = a_{2}

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a_{1} = 4 a_{2}

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Solution

The correct option is B $a_{1} = 2 a_{2}$
Let the accelerations of 4 kg and 8 kg blocks be downwards and rightwards respectively,

By length constraint,
$2 x + z + y = l$

Differtiating twice
$2 \frac{d^{2} x}{d t^{2}} + \frac{d^{2} y}{d t^{2}} = 0$
$⟹ - 2 a_{2} + a_{1} = 0$
$⟹ 2 a_{2} = a_{1}$

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