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(D) Power of the drilling machine,$P = 10\, kW = 10 	imes 10^{3}\, W$.Mass of the aluminium block,$m = 8.0\, kg = 8 	imes 10^{3}\, g$.Time for which

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$103\, ^{\circ}C$

Vedclass · Answer

(D) Power of the drilling machine,$P = 10\, kW = 10 	imes 10^{3}\, W$.Mass of the aluminium block,$m = 8.0\, kg = 8 	imes 10^{3}\, g$.Time for which the machine is used,$t = 2.5\, min = 2.5 	imes 60 = 150\, s$.Specific heat of aluminium,$c = 0.91\, J\, g^{-1}\, K^{-1}$.Total energy supplied by the drilling machine $= P 	imes t = 10 	imes 10^{3} 	imes 150 = 1.5 	imes 10^{6}\, J$.Since $50\, \%$ of the power is lost,the useful energy $\Delta Q$ used to heat the block is $50\, \%$ of the total energy.$\Delta Q = 0.50 	imes 1.5 	imes 10^{6} = 7.5 	imes 10^{5}\, J$.Using the formula $\Delta Q = m c \Delta T$,where $\Delta T$ is the rise in temperature:$\Delta T = \frac{\Delta Q}{m c} = \frac{7.5 	imes 10^{5}}{8 	imes 10^{3} 	imes 0.91} = \frac{750}{8 	imes 0.91} = \frac{750}{7.28} \approx 103\, ^{\circ}C$.Thus,the rise in temperature of the block is $103\, ^{\circ}C$.

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