question_answer

An object of mass \[m\] falls on to a spring of constant \[k\] from height \[h\]. The spring undergoes compression by a length \[x\]. The maximum compression \[x\] is given by the equation:

A) \[m\,\,g\,\,h=\frac{1}{2}k{{x}^{2}}\]

B) \[m\,\,g(h+x)=\frac{1}{2}k{{x}^{2}}\]

C) \[m\,\,g(h+x)=-kx\]

D) \[m\,\,g\,\,h=-kx\]

Correct Answer: B

Solution :

Key Idea: Energy is conserved. From law of, conservation of energy potential energy at height \[h=\] energy stored in compressed spring. \[\therefore \]  \[mgh+mgx=\frac{1}{2}k{{x}^{2}}\] \[\Rightarrow \]                 \[mg(h+x)=\frac{1}{2}k{{x}^{2}}\]