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A mass of 2 kg, initially at a height 1.2 m above an uncompressed spring with spring constant 2 $\times$ 10⁴N/m, is released from rest to fall on the spring. Taking the acceleration due to gravity as 10 m/s² and neglecting the air resistance, the compression (in mm) of the spring in mm is $______$ (given $\sqrt{24} = 5$ )

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answer is 50.

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Detailed Solution

Given,

mass m = 2kg

height h = 1.2m

$s p r i n g c o n s \tan t = k = 2 \times 10^{4} N / m$

we know that,

$m g h = \frac{1}{2} k x^{2} x = \sqrt{\frac{2 m g h}{k}} x = \sqrt{\frac{2 \times 2 \times 10 \times 1.2}{2 \times 10^{4}}} x = \sqrt{24 \times 10^{- 4}} x = 5 \times 10^{- 2} m$

Hence the correct answer is 50.

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