A ball of mass 100 g is dropped from a height $h = 10 cm$ on a massless platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$ . The spring constant is (in N/m) :-

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Energy conservation: gravitational PE lost = elastic PE stored. Depression $x = \frac{h}{2} = 5 cm = 0.05 m$ .

$m g (h + x) = \frac{1}{2} k x^{2} \Rightarrow 0.1 \times 10 \times (0.10 + 0.05) = \frac{1}{2} k (0.05)^{2}$ .

$0.15 = 0.00125 k \Rightarrow k = 120 N/m$ . Answer: 120.

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