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  4. In the system shown in the adjoining figure, the acceleration of 1 kg mass is

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Q. In the system shown in the adjoining figure, the acceleration of 1 kg mass isPhysics Question Image

Laws of Motion

Solution:

If a is downward acceleration of 4 kg block, the upward acceleration of 1 kg block must be 2a.
image
If T is tension in each part of string, then equations of motion of the two blocks are
$4a = 4g - 2T\, ... (i)$
$1 × 2a = T - 1g \,...(ii)$
or $4a = 2T - 2g\, ...(iii)$
Adding (i) and (iii), we get
$8a=2g, a=\frac{g}{4}$
$\therefore $ Acceleration of 1 kg block $=2a=\frac{g}{2}$ upwards.