JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति JEE PYQ - Work Energy Power and Collision

  • question_answer
    A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant \[k=1.25\times {{10}^{6}}N/m.\]The body sticks to the platform and the spring's maximum compression is found to be x. Given that \[g=10\,m{{s}^{-2}},\,\]the value of x will be close to- [JEE Main 11-Jan-2019 Morning]

    A) 8 cm    

    B) 40 cm

    C) 80 cm

    D) None of these

    Correct Answer: D

    Solution :

    (*) The moment 1 kg hits the platform,
    \[1(v)+0=(1+3){{v}_{1}}\Rightarrow |(\sqrt{2gh})|=4{{v}_{1}}\]
    \[\Rightarrow \]\[{{v}_{1}}=\frac{\sqrt{2gh}}{4}=\frac{\sqrt{2\times 10\times 100}}{4}=\sqrt{\frac{{{10}^{3}}}{8}}m/s\]
    (Compression due to masses is negligible.)
    Using energy conservation principle,
    \[\frac{1}{2}Mv_{1}^{2}=\frac{1}{2}k{{x}^{2}};\]
    \[x=\sqrt{\frac{M'}{k}{{v}_{1}}}=\sqrt{\frac{4}{\frac{5}{4}\times {{10}^{6}}}\times \frac{{{10}^{3}}\times {{10}^{4}}}{4}}cm\]\[=2cm\]
    *None of the given options is correct.


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