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  4. A ball of mass 100 g is dropped from a height h =10 cm on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance ( h /2). The spring constant is Nm -1 . (. Use .g=10 ms -2)

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Q. A ball of mass $100 \,g$ is dropped from a height $h =10 \,cm$ on a platform fixed at the top of 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 _____$Nm ^{-1} . \left(\right.$ Use $\left.g=10 \,ms ^{-2}\right)$Physics Question Image

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Solution:

By energy conservation
$PE = KE$
$ mg \left( H +\frac{ H }{2}\right)=\frac{1}{2} kx ^{2}\left( x =\frac{ H }{2}\right)$
$0.100 \times 10 \times \frac{3}{2}(0.10)$
$=\frac{1}{2} k (0.05 \times 0.05) $
$ k =\frac{3 \times 0.10}{0.05 \times 0.05} $
$=\frac{3 \times 1000}{25}=120\,N / m$