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Question

A block of mass 2 kg is dropped from a height of 40 cm on a spring whose force-constant is 1960 Nm1. 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 cm
Given data,
Mass of the body is ( m ) =2Kg
spring's constant (K)=1960N/m
height of the body =0.4m
Let the maximum distance spring will compressed =xm
initial 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=Kx2

Kx22mgx2mgh=0

1960x22×2×9.8×x2×2×9.8×0.4=0

1960x239.2x15.68=0

after solving this quadratic equations , we get x=0.1m

hence, answer is x=0.1m


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