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Question

A body of mass 1 kg moving with a velocity of 5 m/s hits a spring on its free end. The other end of spring is fixed and it has a force constant of 400 N/m. The body comes to rest after compressing the spring by 'x' m, the value of 'x' m is

A
0.55 m
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B
0.35 m
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C
0.45 m
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D
0.25 m
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Solution

The correct option is D 0.25 m
Given u=5 m/s
Force constant k=400 N/m
let x be compression n the spring when body comes to rest.
Applying law of conservation of energy,
KfKi=UiUf
(Kf=0 as final velocity is zero ,Ui=0 as spring is not streched initially)
12mu2=12kx2
x=umk=51400=520=0.25 m

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