Uttarakhand PMT Uttarakhand PMT Solved Paper-2004

  • question_answer
    A machine which is 75% efficient, uses 12 J of energy in lifting 1 kg mass through a certain distance. The mass is then allowed to fall through the same distance. The velocity at the end of its fall is

    A) \[\sqrt{12}\] m/s

    B) \[\sqrt{18}\] m/s

    C) \[\sqrt{24}\]m/s

    D) \[\sqrt{32}\] m/s

    Correct Answer: B

    Solution :

     Potential energy of the mass at a height above the surface is given by \[=\frac{75}{100}\times 12=9J\]           ...(1) Now K.E. of the mass at the end of fall \[K.E.=\frac{1}{2}m{{\upsilon }^{2}}\]          ...(2) Applying law of conservation of energy \[\frac{1}{2}m{{\upsilon }^{2}}=9\] \[\upsilon =\sqrt{\frac{2\times 9}{m}}=\sqrt{\frac{18}{1}}=\sqrt{18}\,m/s\]


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