Application of Newtons laws

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Question

Two blocks are connected by a spring. The combination is suspended, at rest, from a string attached to the ceiling, as shown in the figure. The string breaks suddenly. Immediately after the string breaks, if the initial acceleration of the upper block is found to be ng/2. The value of n is_______

Moderate

Solution

$\begin{array}{l} T = K x + 2 m g . . . . (1) \\ K x = m g . . . . . (2) \\ T = 3 m g . . . . . . (3) \end{array}$
After cutting T = 0
downward net force on 2m block becomes $3 m g$
$∴ a = \frac{3 m g}{2 m} = \frac{3 g}{2}$

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