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Haryana PMT Haryana PMT Solved Paper-1999

  • question_answer
    A bulb of 100 watt is suspended at a height 2      m from the centre of the table. When it is            raised by one metre. The percentage change                in the illuminance at the centre of the table        will be :

    A)  64.4%                                  

    B)  34.4%

    C)  53%                                      

    D)  55.6%

    Correct Answer: D

    Solution :

                    Let I be the luminous intensity of bulb the initial illuminance is: \[E=\frac{I}{{{(2)}^{2}}}\]                    ?..(1) Final illuminance is given by \[E'=\frac{I}{{{(3)}^{2}}}\]                            ..?.(2) Percentage change in illuminance is given by \[\frac{\Delta E}{E}\times 100=\frac{E'-E}{E}\times 100%\]                 \[=\left( \frac{E'}{E}-1 \right)\times 100%\]                 \[=\left[ \frac{{{\left( \frac{I}{3} \right)}^{2}}}{{{\left( \frac{I}{2} \right)}^{2}}}-1 \right]\times 100%\]                 \[=\left( \frac{4}{9}-1 \right)100%=-\frac{5}{9}\times 100%\]                 \[=-55.6%=55.6%\] decrease


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