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Question

A body of mass m dropped from a certain height strikes a light vertical fixed spring of stiffness k. The height of its fall before touching the spring if the maximum compression of the spring is equal to 3mgk is


Correct Answer
A
3mg2k
Your Answer
B
2mgk
Your Answer
C
3mg4k
Your Answer
D
mg4k

Solution

The correct option is D 3mg2k
Change in height of the particle is h+x
where x is compression in the spring

Applying law of conservation of energy
work done by gravity = work stored in spring in the form of potential energy 

mg(h+x)=12kx2     ( x=3mgk maximum compression)
(h+x)=kx22mg 
h=kx22mgx=k(3mg/k)22mg3mgkh=9mg2k3mgk=3mg2k

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