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Displacement

In the pulley...

Question

In the pulley-block arrangement shown in the figure, find the relation between acceleration of blocks A and B.

A

a_{B} = 0.5 a_{A}

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B

a_{B} = - 2 a_{A}

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C

a_{B} = a_{A}

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D

a_{B} = - 3 a_{A}

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Solution

The correct option is D $a_{B} = - 3 a_{A}$
$T_{A} = 3 T, T_{B} = T$
In such type of problems
$a α \frac{1}{T}$
$∴∣ a_{B} ∣= 3 ∣ a_{A} ∣$
or $a_{B} = - 3 a_{A}$ , as $a_{A}$ and $a_{B}$ are in opposite directions.

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