A massless platform is kept on a light elastic spring, as shown in the figure. When particle of mass 0.1 kg is dropped on the pan from a height of 0.24 m, the particle sticks to the pan, and the spring is compressed by 0.01 m. From what height should the particle be dropped to cause a compression of 0.04 m?

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TestHub · Accepted Answer

Let the particle be dropped from a height h and the spring be compressed by y. According to conservation of mechanical energy,
Loss in potential energy of the particle = gain in elastic potential energy of the spring

$∴ mg (h + y) = \frac{1}{2} k y^{2}$

Now, as the particle and spring remain same, hence

$\frac{h_{1} + y_{1}}{h_{2} + y_{2}} = {(\frac{y_{1}}{y_{2}})}^{2}$

$(\frac{0 \cdot 24 + 0 \cdot 01}{h_{2} + 0 \cdot 04}) = {(\frac{0 \cdot 01}{0 \cdot 04})}^{2}$

Solving we get, h₂= 3.96 m

Physics - W.E.P. Question with Solution | TestHub

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