JEE Main & Advanced Sample Paper JEE Main - Mock Test - 38

  • question_answer
    A steel drill making 180 rpm is used to drill a hole in a block of steel. The mass of the steel block and the drill is 180 g each. Consider all the entire mechanical work is used up in providing heat and the rate of rise of temperature of the block is \[0.5{}^\circ C\,{{s}^{-1}}\]. Specific heat of steel is \[0.10\,cal-{{g}^{-1}}{{K}^{-1}}.\]The couple required to drive the drill is

    A) \[20.3\text{ }Nm\]       

    B)        \[37.8\text{ }Nm\]           

    C)     \[31.48\text{ }Nm\]          

    D)        \[2.0045\text{ }Nm\]

    Correct Answer: D

    Solution :

    [d] Thermal power \[P=\frac{dQ}{dt}=mc\left( \frac{dT}{dt} \right)\] \[=(180\times {{10}^{-3}})(0.10)(4200)(0.5)=37.8\,Watt\] Mechanical power \[\rho =r\omega \] \[\tau =\frac{37.8}{\left( 180\times \frac{2\pi }{60} \right)}=2.0045\,Nm\]


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