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5.Work, Energy, Power and Collision
easy
A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k.$ The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be
A
$2 Mg/k$
B
$4 Mg/k$
C
$Mg/2k$
D
$Mg/k$
(AIPMT-2009)
Solution
$\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,When\,the\,mass\,attached\,to\,a\,spring\\
fixed\,at\,the\,other\,end\,is\,allowed\,to\,fall\\
suddenly,\,it\,extends\,the\,spring\,by\,x.\,\\
potential\,energy\,lost\,by\,the\,mass\,is\\
gained\,by\,the\,spring.\\
Mgx = \frac{1}{2}k{x^2} \Rightarrow x = \frac{{2Mg}}{k}.
\end{array}$
Standard 11
Physics
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