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Roatation

In the figure...

Question

In the figure shown all contact surfaces are smooth. Acceleration of block B will be $(g = 10 m / s^{2}) :$

1 m / s^{2}

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2 m / s^{2}

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3 m / s^{2}

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none of these

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Solution

The correct option is C $1 m / s^{2}$
FBD of both the blocks is shown above.
Let the tension in the string be $T$ .
From work theorem, $T x_{A} - 3 T x_{B} = 0$
Or $x_{A} = 3 x_{B}$
Differentiating it twice w.r.t. time, we get
$⟹$ $a_{A} = 3 a_{B}$
For block A :
$m a_{A} = T$
For block B :
$m a_{B} = m g - 3 T$
Or $m a_{B} = m g - 3 (m a_{A})$
Or $m a_{B} = m g - 3 m (3 a_{B})$
Or $10 m a_{B} = m g$
$⟹ a_{B} = \frac{g}{10} = \frac{10}{10} = 1 m / s^{2}$

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