KVPY Sample Paper KVPY Stream-SX Model Paper-8

  • question_answer
    A 10 kW drilling machine is used to drill a bore in a small aluminum block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minute? Assuming 50% of power is used up in heating the machine itself or lost the surroundings specific heat of aluminum \[=0.91J/g-{}^\circ C.\]

    A) \[10.23\text{ }{}^\circ C\]                     

    B) \[23.10{}^\circ C\]

    C) \[103.02\text{ }{}^\circ C\]                   

    D) \[301.02{}^\circ C\]

    Correct Answer: C

    Solution :

    total energy used by drilling machine \[=Pt\]\[=\left( 10\times {{10}^{3}} \right)\times \left( 2.5\times 60 \right)\]\[=1.5\times {{10}^{6}}\operatorname{J}\]
    The energy absorbed by the aluminium block \[=\frac{50}{100}\times 1.5\times {{10}^{6}}\]
    Let \[\Delta T\]be the rise in temperature of the aluminium block, then
    \[mC\Delta T=0.75\times {{10}^{6}}\]\[\left( 8\times {{10}^{3}} \right)\times 0.91\times \Delta T=0.75\times {{10}^{6}}\]
    \[\therefore \Delta T=103.02{}^\circ C\]


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