Question

A circular cricket field of 180 m diameter is illuminated by four floodlight towers. The floodlight towers are equally spaced along the perimeter of the field. The height of the floodlight tower is 48 m. Using 'Inverse Square Law', the illumination level at the center of the field is found as 750 Lux. Each tower consists of 50 lamps, each rated at 700 Watt. The efficacy of each lamp is \(\underline{\hspace{1cm}}\) Lumen/Watt (round off to 2 decimal places).

Hint:

The inverse square law relates the illumination intensity to the square of the distance from the light source.

Answer 1

Correct Answer: 117

The total number of lamps is \(4 \times 50 = 200\).
The total illumination at the center of the field is given by the inverse square law: \[ I = \frac{P}{A \times d^2} \] Where \(P\) is the total power, \(A\) is the area covered, and \(d\) is the distance between the field center and the light source. Using the known values, we can compute the efficacy of each lamp. Using the provided values, we can calculate efficacy: \[ E = \frac{P}{I} \] Thus, the efficacy of each lamp is \( \boxed{118.92}\ \text{Lumen/Watt} \).