A $2.0 kg$ block is dropped from a height of $40 cm$ onto a spring of spring consant $k = 1960 N/m$ . Find the maximum distance the spring is compressed.

0.080 m

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0.20 m

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0.40 m

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0.10 m

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Solution

The correct option is D $0.10 m$
Decrease in gravitational potential energy = increase in elastic potential energy
$∴ m g (h + x) = \frac{1}{2} K x^{2}$
$2 \times 9.8 \times (0.4 + x) = 980 x^{2}$
$7.84 + 19.6 x = 980 x^{2}$
Solving we get $x = 0.1 m$

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