Question

# A block of mass 2 kg is dropped from a height of 40 cm on a spring whose force-constant is 1960 Nmâˆ’1. The maximum distance through which the springs is compressed by:

A
5 cm
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B
15 cm
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C
20 cm
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D
10 cm
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Solution

## The correct option is D 10 cmGiven data,Mass of the body is ( m ) =2Kgspring's constant (K)=1960N/mheight of the body =0.4mLet the maximum distance spring will compressed =xminitial potential energy of body =mg(h+x)final potential energy = spring potential energy =12Kx2 according to the law of conservation of energy,initial potential energy = final potential energy mg(h+x)=12Kx2 2mgh+2mgx=Kx2Kx2−2mgx−2mgh=0 ⇒1960x2−2×2×9.8×x−2×2×9.8×0.4=0⇒1960x2−39.2x−15.68=0 after solving this quadratic equations , we get x=0.1m hence, answer is x=0.1m

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