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A spring–loaded toy gun is used to shoot a ball of mass M straight up in the air. The ball is not attached to the spring. The ball is pushed down onto the spring so that the spring is compressed a distances S below its unstretched point. After release, the ball reaches a maximum height 3S, measured from the unstretched position of the spring (see diagram). The spring constant of the spring is

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Mg/S

2Mg/S

4Mg/S

8Mg/S

answer is D.

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Detailed Solution

$K E_{I} = 0, P E_{I} = \frac{1}{2} k S^{2}$ , Work = 0

$K E_{F} = 0, P E_{F} = M g (4 S) = \frac{1}{2} k S^{2}, M g (4 S)$

$k = \frac{2 M g (4 S)}{S^{2}} K = \frac{8 M g}{S}$

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