question_answer

A bulb of 100 watt is hanging at a height of one meter above the centre of a circular table of diameter 4 m. If the intensity at a point on its rim is \[{{I}_{0}}\], then the intensity at the centre of the table will be                                    [CPMT 1996]

A)            \[{{I}_{0}}\]                          

B)            \[2\sqrt{5}{{I}_{0}}\]

C)            \[2{{I}_{0}}\]                        

D)            \[5\sqrt{5}{{I}_{0}}\]

Correct Answer: D

Solution :

                   The illuminance at B   \[{{I}_{B}}=\frac{L}{{{1}^{2}}}\]        .......(i) and illuminance at point C \[{{I}_{C}}=\frac{L\cos \theta }{(\sqrt{5{{)}^{2}}}}=\frac{L}{(\sqrt{5{{)}^{2}}}}\times \frac{1}{\sqrt{5}}\] \[\Rightarrow \ \ {{I}_{C}}=\frac{L}{5\sqrt{5}}\]      ...... (ii) From equation (i) and (ii)   \[{{I}_{B}}=5\sqrt{5}\ {{I}_{0}}\]