NEET Sample Paper NEET Sample Test Paper-21

  • question_answer System shown in the figure is released from rest. Pulley and spring are massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring K = 40 N/m and\[g\text{ }=\text{ }10\text{ }m/{{s}^{2}}\])

    A) \[\sqrt{2}\,m/s\]                      

    B) \[2\sqrt{2}\,m/s\]        

    C)   \[2\,m/s\]         

    D)   \[4\sqrt{2}\,m/s\]   

    Correct Answer: B

    Solution :

    Hence, the correction option is (a).              Let \[x\]be the extension in the spring when 2 kg block leaves contact with the ground. \[\therefore \]\[Kx=2g\]or \[x=\frac{2g}{K}=\frac{2\times 10}{40}=\frac{1}{2}m\] From conservation of mechanical energy (for m = 5 kg block),             \[mgx=\frac{1}{2}K{{x}^{2}}+\frac{1}{2}m{{v}^{2}}\]             \[5\times 10\times \frac{1}{2}=\frac{1}{2}\times 40\times {{\left( \frac{1}{2} \right)}^{2}}+\frac{1}{2}\times 5{{v}^{2}}\]             \[25=5+\frac{5}{2}{{v}^{2}}\]             \[v=\sqrt{8}=2\sqrt{2}\,m/s\] Hence, the correction option is (b).

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